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Decision-Making and Vulnerability in a Pyramid Scheme Fraud
Stacie A. Bosley,a Marc F. Bellemare,b Joshua York,c and Linda Umwalid
February 2018
Abstract: Consumer financial fraud is costly to individuals and communities yet academic research
on the subject is scarce, in part due to how difficult it is to find reliable data. Using a lab-in-the-field
artefactual experiment, we study judgment and decision-making as well as the correlates of
victimization in a prototypical pyramid scheme fraud. We record demographic, psychological,
cognitive, and behavioral characteristics for 452 subjects at the 2017 Minnesota State Fair, and we
estimate the impact of an information treatment—specifically, a reminder to pay attention to the
odds of winning or losing—on our subjects’ behavior in relation to pyramid scheme fraud. Our
results indicate that this straightforward, simple treatment reduces fraud uptake, but only for
subjects with a post-secondary education. Our findings show correlates of victimization beyond
cognitive ability, including impulsivity, risk preferences, religiosity, and prior exposure to pyramid
scheme fraud. Subject reliance on probabilities in decision-making and the accuracy of subjective
expectations are the most statistically significant predictors of the decision to invest in a fraudulent
pyramid scheme. Our results can help inform the targeting of consumer protection interventions as
well as the potential content of those interventions.
a Associate Professor, Economics, Hamline University, [email protected].
b Associate Professor, Applied Economics, University of Minnesota, [email protected].
c Student, Hamline University.
d Sudent, Hamline University.
2
Decision-Making and Vulnerability in Pyramid Scheme Fraud
1. INTRODUCTION
Consumer financial fraud is costly, multifaceted, and difficult to stamp out. The direct, measurable
costs of consumer financial fraud are estimated to be about $45 billion annually in the US (Deevy,
Lucich and Beals 2012). Moreover, such fraud is underreported and its costs extend beyond the
financial to include social, psychological, as well as forgone time and income, and enforcement as
well as regulatory costs that typically go unaccounted for. This means the available cost estimates
are a lower bound on the true costs of consumer financial fraud.
Fraud research is made difficult due to a dearth of reliable data and by the fact that there are
several varieties of consumer fraud. Each type of consumer financial fraud has different
characteristics, methods of persuasion, and target groups. While the stereotype of a typical fraud
victim is that of an older consumer acting out of fear or greed, prior research suggests that there is
no representative set of characteristics defining the likely consumer fraud victim (Knutson and
Samanez-Larkin 2014, Pak and Shadel 2011); some individuals can be susceptible to one form of
fraud while being immune to another.
This article focuses on pyramid schemes.1 The Federal Trade Commission (FTC) estimates that
about two million individuals in the US fall victim to pyramid schemes and related fraudulent
1 Pyramid schemes are usually presented to consumers as chain letters, gifting schemes, or multilevel marketing business opportunities (MLMs). Chain letters are messages that encourage the recipient to send the message along to others, forming a chain of receivers and senders, so long as the receivers comply. When a chain letter is used to propagate a pyramid scheme, it asks the recipient to take an action, usually to send money, and then pass the message on to others who will do the same—pay and send on—with the promise of future returns. While these messages were historically sent as physical letters, they are now often communicated through email or in other digital forms. A gifting scheme is like a chain letter, but the pay-and-recruit offer is framed as giving a “gift” in order to receive a larger benefit in the future. The gift (i.e., the currency of the scheme) can be money or other purchased goods such as books or wine. When a pyramid scheme is disguised as an MLM, the recruit is told she can earn money from the sale of goods or services and
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business opportunities each year (Anderson 2013). Of all victim groups monitored, victims of
pyramid schemes are the least likely to report they have been defrauded (Anderson 2004), making
prevention and enforcement even more important. Harm is compounded by the incentive structure
of most pyramid schemes, as new recruits are trained and incentivized to bring friends and family
into the scheme, leading to broader harm within social networks and communities. As with Ponzi
schemes, trust and affinity often play a significant role in the diffusion of pyramid schemes (Carey
and Webb 2017). In marginalized or vulnerable communities, the ramifications of pyramid scheme
collapse can be dramatic and long-lasting (Fairfax 2003, Gunn 2015, Jarvis 1999). The FTC launched
an initiative in 2016 to combat affinity-based consumer fraud,2 especially within Latino and
African-American communities (Federal Trade Commission 2016), and the Securities and Exchange
Commission launched a Pyramid Scheme Task Force in 2014 in response to evidence of increasing
pyramid scheme activity (Ceresney 2016). Recent pyramid schemes—some targeting teenagers and
young adults—have promoted a fraud offer nearly identical to the scheme we utilize in this
research (Belanger 2018, Fair 2016, Smith 2018).
We explore judgment about, decision-making processes surrounding, and the correlates of
pyramid-scheme victimization using an artefactual field experiment. Past fraud research has often
relied on complaint data or consumer survey methods. Complaint data is plagued with several
forms of selection bias as victims must be able to recognize themselves as being defrauded, be
willing to admit this to others, and proactively provide information to formal reporting agencies.
While survey research does not require consumers to formally report fraud, it still suffers from
underreporting (Deevy, Lucich, and Beals 2012). Analysis of self-reported data is also complicated
from the recruitment of additional sellers. The MLM acts as a pyramid scheme if earnings are dominated by recruitment rewards rather than commissions from retail sales (i.e., sales to those outside the organization; Vander Nat and Keep 2002). 2 Affinity-based fraud is promoted person-to-person, capitalizing on pre-existing social connections and high levels of in-group trust (Perri and Brody 2012). As pyramid scheme participants are instructed and incentivized to sell the “opportunity” to others, affinity groups such as religious or immigrant communities or fraternal organizations make fertile ground for scheme diffusion (Bosley and Knorr 2018).
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by variation in past exposure to consumer financial fraud, and a consumer’s likelihood of being
exposed to a type of fraud is not necessarily correlated with her susceptibility to that form of fraud
(Schoepfer and Piquero 2009). To bypass self-reporting altogether, researchers have created
survey-based fraud susceptibility measures but acknowledge that these measurements will deviate
from lived experiences in nontrivial ways (James et al. 2014). The gold standard is data that directly
confirms fraud victimization and allows for comparisons with non-victims.
Fraud research is also difficult because of the problem posed by accurately attributing
consumer vulnerability to its possible sources. Past research has looked for demographic correlates
of fraud vulnerability or associations between victimization and psychological or behavioral
characteristics such as impulsivity, risk preferences, or financial literacy (Deevy, Lucich, and Beals
2012). While not directly exploring consumer fraud, a related strand of research has explored
relationships between individual characteristics and decision-making processes (e.g., age and
cognitive processes in Besedes et al. 2012), with an eye toward potential vulnerability in the
marketplace. Very few studies have explored both decision-making processes and individual
characteristics in the realm of consumer fraud. Exceptionally, Knutson and Samanez-Larkin (2014)
studied investment fraud and noted the need for additional research in this vein, within different
consumer fraud contexts, to identify “promising targets for intervention” and inform the nature of
the interventions themselves.
Our lab-in-the-field experiment was designed to explore judgment and decision-making
associated with pyramid scheme fraud as well as the correlates of victimization. The experiment
was conducted over two days at the 2017 Minnesota State Fair with 452 subjects. Following Cubitt,
Starmer, and Sugden (2001), we use a one-shot, single-task, individual-choice design to explore
decision-making in this context. All participants were exposed to the same fraud offer; they could
choose to either keep a certain amount of money or to invest that sum in a gamble (i.e., the
5
fraudulent pyramid scheme offer).3 To test a potential policy intervention, our treatment group
received a reminder to weigh the odds of winning or losing before making their choice. We
collected data on demographic, behavioral, and psychological factors, and we asked questions that
probed the individual’s judgments (e.g., the perceived likelihood of “winning” within the fraudulent
offer) and decision-making processes (e.g., reliance on probability in choice). We also collected
information on prior exposure to pyramid scheme fraud, but only after a debrief, so as to not prime
our subjects.
The contribution of this paper is fourfold. First, our experimental design allows for a
comparison between victims and nonvictims that is untainted by differences in exposure to the
pyramid-scheme fraud we study. As the subjects were given a specific and real-life choice with
financial incentives, risk factors and decision-making processes can be identified that may be
unique to this specific form of fraud and very difficult to capture through complaint data or pure
surveys. Second, the data allow exploring systematic pitfalls in judgments as well as implications
for behavior. Third, the experimental treatment allows evaluating the impact of a simple potential
policy intervention. Lastly, this work identifies potential profiles of vulnerable individuals which
can help better target pyramid scheme fraud prevention efforts.
The remainder of this article is organized as follows. Section 2 describes the experimental
framework in more detail. Section 3 presents the data generated by the experiment while Section 4
outlines our empirical framework and identification strategy. Section 5 provides results and
compares findings to past fraud research. Section 6 concludes with policy implications and
directions for future research.
3 We discuss the ethics of our experiment and IRB approval in section 2.
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2. EXPERIMENTAL FRAMEWORK
To study behavior in the context of pyramid scheme fraud, we designed a choice task with two
mutually exclusive options. Immediately following the consent process, subjects were asked to
select option A and keep the $5 given to them4 or select option B and invest that $5 in the Airplane
Game, a hypothetical game which we designed to reflect the features of an actual pyramid scheme
(Neuffer 1987). Figure 1 provides a visual representation of the options as they were presented to
subjects. Essentially, option B is a gamble with potential payoffs of $10 with probability 0.01 or $1
with probability 0.99, and it is a simulated pyramid scheme—no actual recruitment of others is
required—whose likelihood of winning is based on the rules provided. To determine the likelihood
of winning, subjects need to accurately process the rules of the game.
Figure 1. Choice Task
4 We provided cash at the outset and told our subjects that it was theirs to mitigate a potential “house money” effect, wherein subjects are more inclined to take on more risk than they otherwise would because they mistakenly believe they are using the experimenter’s money.
7
As a prototypical pyramid scheme, the Airplane Game has a pay-and-recruit structure that is
inherently deceptive, and thus illegal outside of the laboratory. The exponential structure is
designed to pass money from losers to winners (typically based on time of entry), with the vast
majority in a loss position at every point in the life of the scheme (Vander Nat and Keep 2002). Two
key factors define the pyramid structure: (i) the number of recruits needed for any single
participant to “win,” and (ii) the current number of levels. Figure 2 represents the pyramid
described in our offer, with width and depth dictated by these two factors. In the context of our
Airplane Game offer, a participant would need to have 39 recruits (31 + 32 + 33) to become a Captain
and win the $10 payoff. But they are not alone: since there are already 40 individuals in the game,
the new participant would be entering at the fourth level of the structure. Taking these facts and the
additional simplifying assumptions into consideration, subjects should come to a determination
that the probability of winning (i.e., becoming Captain) is effectively zero as the number of needed
hypothetical recruits exceeds the eligible hypothetical population.5 Subjects were told they could
write on the choice task paper as desired and many ultimately drew pyramid structures and
showed evidence of basic calculations.
Figure 2. Pyramid Scheme Structure
5 As the number of participants at level n is 3n (with recruitment factor of 3 for this pyramid scheme), the number of cumulative participants at level n can be represented as ∑ 3𝑥𝑥𝑛𝑛
𝑥𝑥=0 . Entering the game at the fourth level, sufficient recruits are needed through the seventh level to become a Captain. At the seventh level, the cumulative number of participants required exceeds the finite population provided in the Airplane Game offer. Given that this is a hypothetical game, participants cannot adjust their recruitment speed to secure needed recruits before the population is exhausted and all participating subjects are assumed to have the same recruitment cost function, meaning that all participants recruit with equal speed, effort and success.
8
Subjects were randomly sorted into control and treatment groups based on odd or even subject
identification numbers. The treatment group was shown a reminder of the odds salience at the top
of the choice task handout, which stated: “Throughout this experiment, think carefully about your
odds of winning each option before choosing”; the control group was not shown that reminder. The
remainder of the experiment was identical for both the treatment and control groups.
Following the one-shot, individual choice task, each subject responded to a series of survey
questions. Subject dividers and instructions prevented communication with other subjects and with
those outside the experiment. As described in Deevy, Lucich, and Beals (2012), fraud research
typically explores demographic, behavioral, situational, psychological and cognitive correlates.
Figure 3 outlines the survey questions6 in our experiment and, where appropriate, relevant sources
or the corresponding literature. Beyond basic demographic information, the household ZIP code
allows us to identify whether the subject’s place of residence is urban or rural. To measure risk
preferences, we used the DOSPERT Scale (Blais and Weber 2006) which solicits risk attitudes
within domains most relevant to the realm of inquiry—in this case, within the domains of financial
investment and gambling. The DOSPERT Scale captures the subject’s willingness to take risks, the
perceived benefits of taking those risks, as well as perceptions of the level of risk in three types of
investments (speculative stocks, business ventures, and moderate growth funds) and three types of
gambling (sporting events, horse races, and casinos or poker).
Research indicates a potential role for religiosity and recent negative life events in fraud
vulnerability (Bosley and Knorr 2018, Anderson 2013). We included two religiosity questions from
the Pew Religious Landscape Study (Pew Research Center 2014), viz. degree of religiosity and
6 See Appendix B for the full set of survey questions, the experiment protocol, and the choice task handout given to subjects.
9
frequency of service attendance, and the same negative life event question as in the FTC Fraud
Survey (Anderson 2013).
Figure 3. Survey Components
To measure cognitive ability, we use a three-item cognitive reflection test (CRT; Frederick
2005). As this test has been widely used in research, we only made superficial modifications to the
•Gender•Age•Education•Race/ethnicity•Household Income•Political Affiliation (Pew Research Center 2017)•ZIP code: used to compute percent urban population in ZIP code of residence (created from US Census
Bureau ZCTA data and County Classification Lookup Table - 2010)
Demographics
•Risk-taking: domain-specific attitude questions in investment and gambling, capturing willingness to take risks, perceived benefits of taking risks, and perceived riskiness of investments and gambling (Blais and Weber 2006)•Religiosity: degree of religiosity and religious service attendance (Pew Research Center 2014) •Negative life events: adapted from FTC Fraud Survey question (Anderson 2013)•Prior exposure: self or friend/family member have been pitched or participated in a pyramid scheme in
the past
Behavioral/Situational
•Cognitive ability: adapted from three-item Cognitive Reflection Test (Frederick 2005)•Impulsivity: 11-item Barrett Impulsivity Scale Non-Planning questions (Knutson and Samanez-Larkin
2014; Patton, Stanford, and Barratt 1995) and impulsive, incorrect answers from Cognitive Reflection Test (Frederick 2005)•Financial Literacy: three questions from FTC Fraud Survey (Anderson 2013)
Psychological/Cognitive
•Number of recruits needed to become a Captain (choices: 3, 9, 27, 39, 40 or more)•Number of people also (concurrently) recruiting to become a Captain (open answer)•Perceived chance of becoming a Captain (choices: 50% or above, 40-49%, 30-39%, 20-29%, 10-19%, 5-
9%, below 5%) - we will refer to this as Perceived Win Likelihood or PWL•How much chances of becoming a Captain (i.e., likelihood of winning the Airplane Game) influenced
choice task decision (seven-point Likert scale from Not at All to Extremely) - we will refer to this as Reported Role of Perceived Win Likelihood or RRPWL•Perception of Airplane Game as legal or illegal
Airplane Game Processing
10
three questions.7 The CRT questions are designed to call to mind a quick, incorrect answer though
the correct answer is not difficult to compute. The answers can therefore be used to compute a
“number of correct answers” score and a “number of impulsive answers score,” or iCRT score. In
addition to the iCRT score, we follow Knutson and Samanez-Larkin (2014) and include the non-
planning questions from the Barratt Impulsivity Scale, a commonly used instrument to measure
impulsivity (Patton, Stanford, and Barratt 1995). Beyond general cognitive ability and self-control,
we captured financial literacy using three questions from the FTC Fraud Survey (Anderson 2013).
Two of the three questions are quite basic and capture basic numeracy, a requisite skill for financial
literacy, while the third captures specific financial knowledge (compound interest).
Lastly, we ask questions specific to this fraudulent pyramid scheme offer. These questions are
designed to explore the subject’s judgment and decision-making processes in this unique context.
Participants kept the choice task (i.e., option A or B) handout throughout the experiment and were
encouraged to revisit it when answering these questions. Within this set of questions, we capture
the subject’s perceived likelihood of winning the Airplane Game, which we refer to as “Perceived
Win Likelihood” (hereafter PWL). We also ask subjects to report the role that this perceived
likelihood played in the choice task (i.e., uptake) decision, and to this as the “Reported Role of
Perceived Win Likelihood” (hereafter RRPWL).
Two short debrief videos followed these survey questions. The first video discussed the
Airplane Game as a form of fraud as well as the inherent deception and illegality of pyramid
schemes. It also included a breakdown of the actual likelihood of winning and informed participants
who chose option B (i.e., the Airplane Game) that they would be given a 1% chance of winning the
$10 (drawing from 1 green marble and 99 red marbles) in our experiment. The second video
discussed the multiple forms of pyramid schemes in the marketplace, including gifting schemes and
7 For example, in one question “machines” and “widgets” are changed to “ovens” and “pizzas.” Approximately 16% of experiment subjects indicated that they had seen similar questions at some time in the past.
11
fraudulent business opportunities, and provided warning signs of pyramid scheme fraud. After the
debrief, subjects were asked about their prior exposure to pyramid schemes.
Finally, if the subject chose option A, she simply kept the $5. If the subject chose option B and
invested in the Airplane Game, she returned the $5, drew a marble, and was paid accordingly ($10
for a green marble, $1 for red marble, with the probabilities being respectively 0.01 and 0.99). Each
subject left with an educational brochure that included resources and warning signs of pyramid
scheme fraud.
The experiment was conducted as part of the University of Minnesota Driven to Discover
research initiative at the 2017 Minnesota State Fair. A designated facility housed multiple
university-related research projects of various types, and fairgoers voluntarily entered to
participate in one or more experiments of their choosing. In our case, fairgoers were eligible
subjects if they were 18 or older and had basic English language proficiency. A total of 452 people
ultimately participated in the experiment. The experiment was about 20 minutes in length.
Because of its nature, the project was reviewed extensively by the university’s institutional
review board. The fraudulent offer presented within the choice task was modeled after offers that
appear in the daily lives of consumers and adult subjects were only allowed to participate if they
demonstrated minimum English proficiency. The debrief videos and take-home resources were
created to inform consumers on the illegality of the Airplane Game in particular and to illustrate the
warning signs of pyramid scheme fraud more broadly. Many participants commented on the
educational value of the experience and voluntarily related prior experiences they had with
pyramid scheme fraud.
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3. DATA
Summary Statistics
Table 1 provides subject characteristics along with uptake percentage, i.e., the share of subjects
who chose to invest money in our stylized pyramid scheme. Nearly 91% of experiment participants
were from Minnesota with another 3.6% from Wisconsin and the remainder from other states, so
we compare subject characteristics to Minnesota data from the U.S. Census Bureau (2016). Our
sample differs from the state’s demographic profile most significantly in terms of gender, age,
education, and in whether subjects live in rural or urban areas. As is common in voluntary survey
research, women represent an outsized share of the subject pool (Sax, Gilmartin, and Bryant 2003).
While about 18% of Minnesotan adults are aged 65 or older, this age cohort constitutes only 5% of
our sample. In terms of education, about one third of Minnesotans 25 or older hold a Bachelor’s
degree or above while over two-thirds of our participants have attained this level of higher
education. There are also differences in place of residence (i.e., rural or urban). Our participants live
in ZIP codes that are 89% urban, on average, while 73% of Minnesota’s population is classified as
urban, which likely reflects the urban location of the Minnesota state fairgrounds. Approximately
56% identify or lean toward the Democratic party, which likely reflects the urban orientation of the
subject pool.
Our subjects more closely reflect the income, race and ethnicity profile of the state. Median
household income in Minnesota was just over $60,000 in 2015 and the median household income
for our sample was $60,000-$80,000, though a large number of subjects fell within the highest
income category. The share of Caucasian and Hispanic experimental subjects matched their
respective shares in the state at large. We keep these differences and similarities in mind as we
consider relevant sampling weights for external validity, even in the face of the self-selected (i.e.,
13
nonrandom) nature of our sample. In Section 5, we use population-based sampling weights based
on the ZIP code of residence for Minnesota subjects and present associated results.
Overall, 44% of subjects chose to invest money in the pyramid scheme. While it is difficult to
draw conclusions from differences in uptake without holding other observable confounders
constant, a naïve comparison indicates a lower vulnerability to our pyramid scheme for older, male,
graduate school educated, and rural residents. Those in the lowest and highest income categories
are also least likely to invest in the scheme. These results, on their face, contradict the commonly
held stereotype of fraud victims as uneducated, older consumers (Deevy, Lucich, and Beals 2012),
especially given the relatively high uptake among participants with a Bachelor’s degree.
Table 2 provides summary statistics for the remaining survey questions. The average subject
reports a moderate preference for investment risk, a low desire to gamble, and identifies as
somewhat religious. Nearly half of subjects experienced a significant negative life event in the past
two years. In terms of prior experience, a little over half of our subjects have already been exposed
to pyramid schemes through a friend or family member (i.e., the friend or family member was
pitched or joined a scheme) while 30% have direct personal experience with a pyramid scheme. In
terms of cognitive ability and literacy, the average respondent answered one of three CRT questions
correctly, answered one of those CRT questions with the impulsive, incorrect answer, and
answered two of the three financial literacy questions correctly. With a mean question score near
two, the Barratt Impulsivity Scale responses indicate occasional impulsivity in non-planning
domains (i.e., self-control and cognitive complexity) for the average subject (Patton, Stanford, and
Barratt 1995).
Judgment and decision-making in this context could be affected by the perception of the offer as
legal or illegal (Blaufus et al 2016). After all other survey questions and immediately before debrief,
subjects were asked to judge the legality of the Airplane Game. Approximately half of subjects
14
indicated that the scheme was legal. Separate from the judgment pitfalls discussed below, this
figure indicates that basic education on the warning signs of pyramid scheme fraud had not fully
reached this relatively educated sample prior to the experiment.
Pitfalls in Judgment
When asked to process the rules of the Airplane Game, about half of subjects correctly identify the
number of recruits needed to become Captain and a similar share identify the minimum number of
concurrent recruiters, but only 31% answer both questions correctly. Subjects are also asked to
estimate the likelihood of winning the Airplane Game assuming they were to invest in the game
(whether they actually did so in the choice task or not).
Figures 4 to 6 provide additional information on the Perceived Win Likelihood (or PWL), the
number of needed recruits, as well as the reported role of perceived win likelihood in the choice
task (or RRPWL). Figure 4 reveals the degree to which subjects overestimate the likelihood of
winning the Airplane Game. Recall that the objective probability of winning (i.e., becoming a
Captain) is less than one percent. While about one in four correctly understood that there is a very
low chance of winning (i.e., less than a 5%), a majority of subjects are much more optimistic. Those
who reject the fraud offer tend toward pessimistic expectations and, of those who invest in the
Airplane Game, the largest group estimates the chance of winning at 50% or more.
One potential source of error in judgment is the ability to process the operational rules of the
pyramid scheme. Recall that 51% of subjects failed to recognize that at least 40 people would also
be recruiting, though it was clearly stated that there were already 40 people in the Airplane Game,
and all participants actively recruit. Nearly the same proportion (52%) did not understand that
they would need at least 39 recruits to become Captain. Figure 5 shows the distribution of subject
responses with respect to this question, where the possible options reflect the most likely numeric
errors in this context (e.g., answering only three—counting direct recruits only—or 3 × 3 × 3
15
rather than 3 + (3 × 3) + (3 × 3 × 3). These findings point to common pitfalls in judgment that
are unique to this specific form of fraud. If a consumer does not have the skills needed to
understand the operational rules of the scheme, they are likely to significantly overestimate the
likelihood of profit.
Figure 4. Perceived Win Likelihood (or PWL)
118
97
21
61
41
20
75
41
34
67
30
3736
14
22
32
15 17
63
14
49
O V E R A L L U P T A K E = 0 U P T A K E = 1
NU
MBE
R O
F SU
BJEC
TS
PERCEIVED LIKELIHOOD OF WINNING THE AIRPLANE GAME
Below 5% 5-9% 10-19% 20-29% 30-39% 40-49% 50% or More
26.1% Correct 38.5% Correct 10.5% Correct
16
Figure 5. Reported Number of Recruits Needed to Win the Airplane Game
One might expect that those who consider the likelihood of winning or losing more heavily
during the choice task would demonstrate better understanding of the Airplane Game and generate
a more accurate assessment of the likelihood of winning. Figure 6 shows that 35% of subjects (161
of 452) indicate that the likelihood of winning has very little or no impact on their uptake decision
while a similar share (i.e., 38%) report that that perceived win likelihood has quite a lot to an
extremely high impact. Interestingly, the distribution for those who reject the fraud offer is
somewhat bimodal, with 42% in the highest two categories (i.e., indicating that the likelihood of
winning is very important to their uptake decision) while 29% are in the lowest two categories.
Those who invest in the Airplane Game typically report that perceived win likelihood played a small
role in their uptake decision. While this does not tell us precisely how much cognitive attention
subjects devoted to probability estimation during the choice task, these responses give us some
insight into the role of subjective probability in the decision-making process.
46
26
20
50
26 24
139
73
66
217
127
90
O V E R A L L U P T A K E = 0 U P T A K E = 1
NU
MBE
R O
F SU
BJEC
TS
NUMBER OF RECRUITS NEEDED TO WIN
3 Recruits 9 Recruits 27 Recruits 39 or More Recruits
48.0% Correct 50.4% Correct 45.0% Correct
17
Figure 6. Reported Role of Perceived Win Likelihood (RRPWL)
4. EMPIRICAL FRAMEWORK
Our core equation of interest is:
Y1i = α1 + β1xi + γ1di + η1gi + ε1i (1)
where yi is a dummy variable equal to one if subject i chose to invest in Airplane Game and equal to
zero otherwise, xi is a vector of individual characteristics that include all elements reflected in
Figure 3 (behavioral, situational, cognitive, and psychological),8 di is a variable equal to one if the
subject was in the (information) treatment group and equal to zero otherwise, gi includes variables
that capture the subject’s knowledge and judgments about the Airplane Game including PWL
(Perceived Win Likelihood) and RRPWL (Reported Role of Perceived Win Likelihood), and εi is an
8 All survey elements are included with the exception of religious service attendance given the high correlation between service attendance and religiosity (𝜌𝜌=0.79).
68
39
29
93
34
59
74
19
55
47
19
28
44
34
10
65
54
11
61
53
8
O V E R A L L U P T A K E = 0 U P T A K E = 1
NU
MBE
R O
F SU
BJEC
TS
REPORTED IMPACT OF PERCEIVED WIN LIKELIHOOD ON UPTAKE DECISION
Not at all Very little Somewhat Moderately Quite a lot Very much Extremely
18
error term with mean zero. Since it is not necessarily the case that a subject exposed to the
information treatment will use that information, the estimate of γ measures the intent to treat
(ITT), and treatment heterogeneity is explored through interaction of treatment with controls.
While xi captures pre-treatment variables, knowledge and judgments about the Airplane Game are
considered to be post-treatment variables so treatment effects are estimated with and without
post-treatment variables.
Beyond the ITT and treatment heterogeneity across control variables, we consider the potential
direct and indirect effects of treatment. In this experiment, it is possible that the treatment has a
direct effect on uptake if a reminder to think about the likelihood of winning directly impacts
uptake behavior. The treatment might also impact uptake indirectly through its effect on the
decision-making variables, PWL and RRPWL, and the subsequent impact of those variables on the
final uptake decision. Therefore, we follow Acharya, Blackwell and Sen (2016) and consider the
possibility that PWL and RRPWL act as mediating variables and estimate the controlled direct effect,
or CDE, of treatment on uptake. The authors define CDE as “the causal effect of a treatment when
the mediator is fixed at a particular level.” We follow Acharya, Blackwell and Sen’s process for
estimating CDE and present results in the following section.
In order to better understand decision-making regarding uptake, we further explore the
mediating variables by estimating the following:
RRPWLi = α2 + β2xi + γ2di + ε2i (2)
PWLi = α3 + β3xi + γ3di + λ3hi + ε3i (3)
where hi includes all variables that capture the subject’s knowledge and judgments about the
Airplane Game including RRPWL (Reported Role of Perceived Win Likelihood) with the exception of
PWL itself. For the analysis of uptake in equation (1), we use a linear probability model with and
without bootstrapping, but we also compare these results to probit and logistic estimation results.
19
Similarly, we estimate equations (2) and (3) using OLS regression but compare results with ordered
probit and ordered logit results. Lastly, we use sample weights based on the population of the
subject’s ZIP code of residence, using data for all subjects residing in Minnesota. The results section
discusses the LPM and OLS results but each table identifies similarities and differences found using
alternative estimation methods. Identification of the treatment’s causal effect on uptake is achieved
through the experimental design and the randomization of treatment assignment. Beyond analysis
of treatment, we explore the correlates of the decision-making variables, PWL and RRPWL, as well
as correlates of fraud uptake.
5. RESULTS
Treatment
We first examine treatment effects for a potential policy intervention aimed at highlighting the
(usually low) odds of making money from a pyramid scheme. In our experiment, subjects were
randomly assigned to control and treatment groups using odd and even subject identification
numbers.9 The treatment consisted of a reminder to pay attention to the likelihood of winning
when making choices within the experiment and took the form of a single sentence, in bold font, at
the top of the choice task handout (image of the treatment statement is available in Appendix B.3 in
the experiment protocol). Table 3 provides characteristics of the control and treatment groups,
with tests for differences in group means. There are no statistically significant differences in group
demographic characteristics, with the exception of political party affiliation. With 14 variables in
that table, it is no surprise that the means for one of them are significantly different, as we would
expect this to randomly be the case for roughly one in 10 variables.
9 Due to a temporary technical issue with our survey software, subject identification numbers were not captured for 82 subjects but this issue did not affect the randomization of group assignment.
20
Table 3 indicates that there are no significant differences in decision-making or judgment (i.e.,
PWL or RRPWL) or uptake behavior between the control and treatment groups. Table 4 presents
regression results that examine the association between the treatment and uptake, controlling for
other potential factors. Consistent with Table 3, results indicate that this straightforward treatment
does not appear to influence behavior, though the ITT estimate of -0.066 is negative as expected in
the first specification. While the treatment coefficient is lower in magnitude, the overall finding is
unchanged in the second specification which removes any possible post-treatment variables.
As discussed in the previous section, it is possible that the treatment could affect the mediating
variables, PWL and RRPWL, creating the potential for an indirect impact on uptake. With respect to
RRPWL, it seems reasonable that the treatment would elevate the role that likelihood plays in the
uptake decision-making process. Furthermore, the treatment could increase the cognitive attention
given to likelihood estimation without affecting the subject’s conscious assessment of RRPWL. If so,
the treatment group could have more accurate assessments of the likelihood of winning the
Airplane Game. To control for possible indirect effects of treatment operating through the
mediating variables PWL and RRPWL, we follow Acharya, Blackwell and Sen’s (2016) procedure to
estimate the controlled direct effect (CDE) of treatment on the dependent variable. The resulting
CDE estimate of treatment on uptake is -0.064 with a bootstrap standard error of 0.047, outside the
range of statistical significance and very close to the ITT results presented in the first specification
of Table 4. In this case, the estimate of treatment effect is effectively the same whether estimated
using the CDE approach or as ITT, controlling for the mediating variables.
Table 5 explores treatment heterogeneity, interacting treatment with control variables. The
consistent finding across the two specifications, with or without post-treatment variables, is the
varied effect of treatment based on educational attainment. The impact of treatment appears to be
significantly different for those with higher levels of education relative to subjects in excluded
group (i.e., those with a high school degree or less) and the treatment-education interaction
21
coefficients are negative, suggesting that this simple reminder to think about the odds of winning
before making decisions might reduce the likelihood of pyramid scheme participation but only
among those with post-secondary education. We consider the policy implications of this finding
further in Section 6.
Correlates of Uptake
Beyond treatment, we consider correlates of fraud uptake to identify potential individual risk
factors. Table 6 presents multiple specifications of uptake analysis where the first specification
includes the full set of regressors. The second and third are reduced specifications, demonstrating
stability (or lack thereof) in statistical significance and direction. As expected, the probability of
investing in the fraudulent offer is negatively associated with RRPWL (i.e., salience of likelihood in
decision-making) and positively related to the PWL. For two identical subjects, the probability of
fraud uptake is eight percentage points higher for the subject with a one-unit higher PWL (e.g.,
where the perceived chance of winning is 20-29% as opposed to 10-19%). The effect size is similar
for RRPWL: there is a seven to eight percentage point increase in the likelihood of uptake for every
one-unit reduction in RRPWL (e.g., when the reported role of likelihood falls from 3-somewhat to 2-
very little). This result is stable across all specifications and estimation methodologies. Attention to
likelihood and accurate assessment of relevant probabilities are associated with reduced personal
vulnerability to pyramid-scheme fraud.
As in other studies of pyramid-scheme fraud (Bosley and Knorr 2018) and lottery fraud
(Consumer Fraud Research Group 2006), religiosity appears to increase vulnerability in this
experiment. On a four-point Likert scale, a one-unit increase in self-reported religiosity is
associated with a five percentage point increase in the probability of fraud uptake. While this
experiment cannot explain the mechanism whereby religiosity and fraud vulnerability are related,
other research points to potential explanations. Bosley and Knorr find a connection between
22
county-level religiosity and pyramid-scheme victimization rates in the US and suggest that religious
communities provide high-trust, clearly defined social networks for recruitment. Subjects with
higher levels of religiosity might be better able to imagine recruitment within their own personal
networks. It may also be that religiosity elevates trust and lessens personal scrutiny at an individual
level, independent of connections to religious social networks or institutions. Table A1 in Appendix
A includes both religious service attendance and religiosity, and only religiosity is statistically
significant when the alternative measure is removed. This provides limited evidence that personal
religiosity may be more relevant to fraud vulnerability than religious social networks, given that
service attendance would presumably enhance ties to church networks more than religiosity itself.
Again, this result is stable across specifications and methods of estimation.
Prior exposure to fraud is another potential risk factor for victimization. We measure prior
exposure to pyramid scheme fraud only after the subject has gone through the debrief process, both
(i) so that subjects understand the variety of ways pyramid schemes are presented to consumers
and the warning signs of this fraud type as well as (ii) to avoid priming our subjects at any time
during the experiment. While personal prior exposure to pyramid scheme fraud is not a significant
predictor of uptake, exposure to a friend or family member who joined or was pitched a pyramid
scheme is associated with an eight to ten percentage point increase in fraud, all else equal As noted
in Section 1, fraud victims are often reluctant to pro-actively report their experience to authorities
and unwilling to admit to having been scammed even when their victim status is independently
verified (AARP 2003, Deevy, Lucich and Beals 2012). There can be a stigma to relating their
experience, even to friends and family, due to embarrassment or confusion around the offer and
outcome. Victims may feel that they were to blame for their own losses due to lack of effort or skill
or feel guilty for bringing others into the scheme. This means that a subject may have been exposed
to pyramid scheme fraud through a friend or family member but not know the outcome of that
23
experience. This exposure then could help to validate the fraud, rather than inoculate the individual
against future victimization.
Controlling for all other regressors, subjects who report higher perceived benefits from risky
financial investments are more likely to invest in the fraudulent offer. While past studies have
identified potential connections between risk-taking and fraud victimization (Anderson 2013,
Schoepfer and Piquero 2009), these studies have not generally identified the risk domain that is
most predictive of fraud uptake which may vary by fraud type.10 These results shed light on the
relationship between fraud and risk by domain: first, the perceived benefits of risky financial
behavior are more predictive than the self-reported willingness to take financial risks or the
perceived riskiness of these financial decisions; second, attitudes toward the investment domain
appear to be more closely connected to pyramid scheme uptake behavior than attitudes toward
gambling. The remaining regressors, including gender, age, education, cognitive ability and
impulsivity, are not statistically significant in the uptake analysis, but may be related to the
subject’s judgment and decision-making as captured in PWL and RRPWL.
Correlates of PWL and RRPWL
Given the desire to explore judgment and decision-making in the context of fraud, the importance of
PWL and RRPWL in uptake behavior, and the central role of likelihood in an expected utility
decision-making framework, we further explore correlates of these variables in Tables 7 and 8.
Subject attention to likelihood in the uptake decision, self-reported in RRPWL, is higher for those
with high cognitive ability and low impulsivity, as measured by the Cognitive Reflection Test and
BIS-Nonplanning scale respectively. While past research has found that fraud victimization is
10 As prior research has challenged the notion of risk preferences as situation-invariant, Blais and Weber (2006) provide a Domain-Specific Risk-Taking (DOSPERT) scale to capture risk attitudes within various situational contexts, or domains of life, such as health, recreation, or finance. Investments and gambling are the two subdomains with the finance domain of the DOSPERT scale.
24
associated with impulsivity and cognitive ability (Deevy, Lucich, and Beals 2012, Knutson and
Samanez-Larkin 2014), our findings suggest that these factors impact behavior through their effects
on decision-making processes and judgment. Cognitive ability and self-control may allow the
subject to pay attention to relevant probabilities and their role in evaluating the gamble which, in
turn, improves accuracy of probability estimates. Attention to likelihood is also higher for those
residing in more urban ZIP codes, all else equal. Past research on the role of rural or urban
residence in fraud vulnerability is mixed, and this finding points to the need for continued research
on the relative vulnerability of urban and rural consumers to different forms of fraud. These
findings hold across specifications as variables are removed.
In terms of the subjective probability of winning, captured by PWL, subjects were more
pessimistic if they reported a larger role for likelihood in decision-making (i.e., higher RRPWL) and
if they understood the correct number of recruits needed to win the Airplane Game. Higher
expectations of winning were associated with higher perceived benefits from gambling and the
perception that the Airplane Game was legal. Again, these findings are consistent across
specifications. Gender and age were nearly statistically significant in the full model, with higher
subjective probability estimates for women and older subjects. Past research has identified
potential gender differences in decision-making under risk that may be relevant in this context. For
example, Helga et. al. (2011) found that men were more likely to use an expected utility decision-
making framework and have more stable subjective probability estimates. This suggests that
women might me more vulnerable than men to pyramid fraud. Past findings on the role of gender
and age in fraud vulnerability are mixed. and this research again suggests a need to replicate the
experiment with an age and gender distribution that more closely reflects the overall population.
Population-based Sample Weights
25
As discussed in Section 3, our sample skewed urban, younger, and more educated than the state of
Minnesota at large. To explore external validity, we adopted sample weights based on the
population of the subject’s home ZIP code, excluding all subjects who were not Minnesota residents
(approximately nine percent of the subject pool). While the introduction of sample weights did not
alter the findings on treatment effects, including the significance of treatment-education interaction
terms, there were some changes in the correlates of PWL, RRPWL and uptake. When the sample
weights are used to more closely reflect the profile of the state, subjects with who identify or lean
toward the Democratic party have lower uptake, everything else equal. Prior exposure to pyramid
scheme fraud through friends or family remains negatively associated with uptake but is no longer
statistically significant. The role of religiosity, perceived benefits of risky financial choices, PWL and
RRPWL in uptake remain the same as in prior results.
Probabilities continue to play a more significant role in the uptake decision for subjects with
higher cognitive ability, lower impulsivity and more urban locations of residence. Beyond these
factors, the subject’s perceived benefit of gambling is now a significant positive correlate of RRPWL,
meaning odds are more salient in the fraud uptake decision for those who anticipate higher benefits
from gambling. Subjects who report higher religiosity also place more weight on likelihood in the
uptake decision, all else equal. Note that this suggests a complex relationship between religiosity
and pyramid scheme fraud, as religiosity is associated with increased attention to likelihood but
also increased uptake.
As before, the estimated likelihood of winning the Airplane Game, PWL, is lower for those who
report a higher role for likelihood in the uptake decision and those who know the correct number
of recruits needed to win, but higher for those who think the offer is legal. There is now a positive
and statistically significant relationship with subject age and a negative relationship with post-
secondary education suggesting that older, less-educated subjects may be more optimistic about
their chances for profit. As discussed in the following section, these results suggest that additional
26
work is needed to replicate this experiment with a more representative sample of consumers, given
the non-random nature of the state fair experimental environment.
Taken together, these results indicate that cognitive ability, self-control, and urban residence
are associated with an elevated role of likelihood in decision-making in this experiment. There is
some indication that religiosity and perceived benefits from gambling may also be related to odds
salience in the context of a pyramid scheme offer. PWL accuracy is, in turn, related to the reported
role of likelihood in decision-making, comprehension of the fraud offer itself, perceptions of
legality, and the perceived benefits from gambling. Perceived likelihood of winning may be inflated
for women or those with less education. These inputs to decision-making, PWL and RRPWL, are
important to the final uptake decision, as are religiosity, perceived benefits from risky investments,
and prior exposure to pyramid scheme fraud through friends or family. The simple treatment—a
reminder of odds salience—appears to reduce fraud uptake but only among those with post-
secondary education.
6. POLICY IMPLICATIONS AND CONCLUSION
This research explores pyramid scheme fraud using an artefactual field experiment, conducted at
the Minnesota State Fair. The ultimate goal is to inform consumer protection efforts by identifying
potential intervention targets (i.e., most at-risk consumers) and by informing the nature and
content of those interventions. As stated at the outset, this work cannot be generalized—research
must be conducted within a specific fraud type as there is no reliable stereotype of the vulnerable
financial fraud victim.
On the potential targets of intervention, this research suggests that those most vulnerable to
pyramid scheme fraud include those with lower self-control and cognitive ability as these
individuals may be less likely to consider odds of winning when making the decision to invest in a
scheme. This may be true of more rural residents as well. Individuals who perceive the offer as
27
legal, who have a poor understanding of the offer itself, who find likelihood of winning to be less
salient, or who perceive greater benefits from gambling tend to overestimate the likelihood of
profit. Those who heavily considered likelihood in the uptake decision and who more accurately
estimated the likelihood of winning were less likely to invest in the fraudulent offer. Beyond these
factors, religiosity, higher perceived benefits from risky investments, and prior exposure are
associated with heightened vulnerability.
These risk factors point to identifiable community-level education targets (e.g., religious or less
educated communities) and to potential ingredients in a personal risk inventory, as suggested by
Knutson and Samanez-Larkin (2014). Such an inventory could include the BIS-Nonplanning
question set, the Cognitive Reflection Test, the DOSPERT scale questions on perceived benefits of
risky gambling and investments, questions about a representative pyramid scheme offer and
legality, as well as questions regarding religiosity and prior exposure.
Beyond identification and discussion of personal risk factors, consumer protection
interventions could teach a multistep approach to offer deliberation. First, the recruit should
scrutinize the offer for warning signs of fraud. As many of our subjects demonstrated (as seen in
Figure 6), it is possible to quickly reject the offer without careful deliberation of odds or other
elements of the offer if one or more warning signs are detected. Warning sign training should be
highly specific to pyramid schemes, the varied forms in which they present themselves, and the
reasons for illegality which are often misunderstood. Second, if no obvious warning sign is detected,
the individual should carefully consider the likelihood of various outcomes with an expected value
mindset, understanding that the recruiter will not necessarily provide reliable evidence of past
earnings or the probability of those earnings. If a recruitment element is involved, special attention
should be paid to the pitfalls in judgment that are unique to this form of fraud, discussed in Section
3.
28
Beyond tailored educational efforts, generalized improvement in educational attainment may
reduce vulnerability, though there is evidence that post-secondary education does not provide
sufficient inoculation in the absence of a treatment like the one implemented in this experiment.
Table 9 depicts the differences in uptake by educational attainment and treatment status without
controlling for other explanatory variables. There were high rates of uptake among college-
educated subjects in the control group, the exception being those with a graduate degree. This
speaks to the need for both educational attainment and continued reminders to deliberately think
through offers in the marketplace. For subjects without post-secondary education, there is some
indication that a reminder to consider the likelihood of winning backfires, as uptake was
substantially higher in the treatment group. It could be the case that greater attention to likelihood
is counterproductive if the decision-maker lacks the skills or knowledge needed to properly
estimate subjective probabilities. This merits further attention with a larger sample size.
Beyond consumer protection efforts aimed at prevention, this research highlights the need for
increased engagement with past victims. Efforts that increase awareness of past victimization and
reduce the stigma of reporting, both formally and informally, will yield positive externalities for
consumers-at-large. As formal complaints often trigger law enforcement action, silence can prevent
detection and response. Informal complaints to friends and family can help to improve
understanding of outcomes. Victim silence may not be neutral, but instead serve to validate the
fraud and increase the risk of future victimization for others within their social networks.
Future research is needed to replicate this experiment, ideally with a nationally representative
sample of consumers. Additional research is also needed on education efficacy, comparing multiple
forms of consumer protection efforts that may include a personal risk inventory. While we suggest
a targeted approach to education and prevention that is informed by the specific nature of pyramid
scheme fraud, it is possible that more generalized consumer protection training would be effective
in preventing pyramid scheme victimization. Lastly, attention should be given to research that
29
investigates and combats pyramid scheme victim silence. While this research indicates potential
avenues for consumer protection, additional research is needed to validate this work and build on
the understanding of pyramid scheme fraud and consumer vulnerability.
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Table 1. Demographic Characteristics and Fraud Uptake
Number of Percent of Uptake Subjects all Subjects† Percentage Total 452 100% 44.2% Gender Men 165 36.5 37.6
Women 286 63.3 48.3 Age Age 18-24 108 23.9 43.5 Age 25-34 86 19.0 50.0 Age 35-44 63 13.9 41.3 Age 45-54 90 19.9 46.7 Age 55-64 76 16.8 39.5 Age 65 or older 23 5.1 34.8
Education High School or Less 42 9.3 52.4 Some College 105 23.2 42.9 Bachelor’s Degree 173 38.3 50.3 Graduate Degree 132 29.2 34.8
Race/Ethnicity Hispanic 22 4.9 50.0 Non-Hispanic 430 95.1 44.0 Caucasian 384 85.0 44.5 Non-Caucasian 68 15.0 42.6
Household Income Less than $20,000 27 6.0 40.7 $20,000-$40,000 62 13.7 53.2 $40,000-$60,000 68 15.0 45.6 $60,000-$80,000 64 14.1 51.6 $80,000-$100,000 68 15.0 47.1 Over $100,000 143 31.6 38.5
Political Affiliation Lean/Identify as Democrat
254 56.2 40.2
Lean/Identify as Independent
50 11.1 50.0
Lean/Identify as Republican
91 20.1 48.4
None of the above 57 12.6 50.9
Percent Urban Less than 25% 25 5.5 40.0 25%-75% 41 9.1 48.8 Over 75% 386 85.4 44.0
† The sum within a group may be less than 100% due to missing data.
33
Table 2. Descriptive Statistics for Non-Demographic Questions
Variable Type Mean Std. Dev
Behavioral/Situational Willingness to Take Risk-Investment Sum of three 7-point
Likert questions 11.41 3.80
Willingness to Take Risk-Gambling Sum of three 7-point Likert questions
4.47 2.88
Perceived Benefit-Investment Sum of three 7-point Likert questions
13.55 3.67
Perceived Benefit-Gambling Sum of three 7-point Likert questions
7.39 4.37
Perceived Risk-Investment Sum of three 7-point Likert questions
13.13 3.09
Perceived Risk-Gambling Sum of three 7-point Likert questions
18.44 3.76
Religiosity 4-point Likert 2.66 1.00 Religious Service Attendance Ordinal, 1-9 4.63 2.40
Negative Life Event Binary 0.45 0.50 Prior Exposure-Self Binary 0.30 0.46
Prior Exposure-Other Binary 0.51 0.50 Psychological/Cognitive
Cognitive Ability-CRT Number of correct answers (3 possible)
1.31 1.08
Impulsivity-iCRT Number of intuitive, incorrect answers
(3 possible)
1.37 1.01
Impulsivity-BIS NonPlanning Sum of eleven 4-point Likert
questions*
20.21 4.26
Financial Literacy Number of correct answers (3 possible)
2.18 0.92
Airplane Game Processing
Correct Number-Recruits Needed Binary 0.48 0.50 Correct Number-Concurrent Recruiters Binary 0.49 0.50
Perceived Win Likelihood (PWL) Ordinal, 1-7 3.42 2.08 Reported Role of Perceived Win Likelihood (RRPWL) 7-point Likert 3.76 2.04
Legal Binary 0.50 0.50 * Uses reverse scoring for certain questions as designated by BIS protocol
34
Table 3. Descriptive Statistics by Experimental Group
Control (n=183) Treatment (n=187) Difference in Means
Mean Std. Error Mean Std. Error Age 39.58 1.169 40.62 1.182 Male 0.385 0.036 0.390 0.036 HS or Less 0.087 0.021 0.086 0.021 Some College 0.240 0.032 0.203 0.030 Bachelor's Degree 0.388 0.036 0.380 0.036 Graduate Degree 0.284 0.452 0.332 0.472 Hispanic 0.044 0.015 0.037 0.014 Caucasian 0.836 0.027 0.856 0.026 HH Income Category 4.099 0.131 4.240 0.120 Democrat 0.492 0.037 0.604 0.036 ** Percent Urban 0.871 0.020 0.898 0.018 Reported Role of Perceived Win Likelihood (RRPWL) 3.787 2.124 3.791 1.998 Perceived Win Likelihood (PWL) 3.328 2.179 3.449 2.014 Uptake 0.475 0.501 0.422 0.495
Note: For each row, the last column presents the results of a t-test of the null hypothesis that the means are equal in both samples. * Difference in means that is significant at the 10% level. ** Difference in means that is significant at the 5% level. *** Difference in means that is significant at the 1% level.
35
Table 4. Estimation Results for Linear Probability Model Analysis of Fraud Uptake – Intent to Treat†
Variables Dependent variable: Uptake (binary)
OLS with post-treatment
variables
OLS without post-treatment
variables Treatment -0.066 -0.035 (1.37) (0.64) Age -0.001 -0.000 (0.66) (0.00) Male -0.024 -0.071 (0.47) (1.22) Some College -0.055 -0.080 (0.57) (0.69) Bachelor's Degree 0.017 -0.006 (0.18) (0.06) Graduate Degree -0.054 -0.110 (0.53) (0.91) Hispanic -0.023 0.000 (0.19) (0.00) Caucasian -0.001 -0.020 (0.02) (0.25) HH Income Category -0.022 -0.023 (1.30) (1.28) Democrat -0.039 -0.075 (0.73) (1.24) Percent Urban 0.029 -0.065 (0.30) (0.58) Willingness to Take Risk-Investment 0.003 0.005 (0.29) (0.56) Willingness to Take Risk-Gambling 0.010 0.010 (1.13) (0.97) Perceived Risk-Investment 0.004 0.001 (0.40) (0.06) Perceived Risk-Gambling 0.008 0.006 (0.91) (0.70) Perceived Benefit-Investment 0.017 0.020 (1.94)* (2.00)** Perceived Benefit-Gambling -0.002 -0.002 (0.22) (0.28) Religiosity 0.050 0.034 (2.04)** (1.20) Negative Life Event 0.072 0.070 (1.47) (1.25) Prior Exposure-Self -0.059 -0.072 (0.99) (1.08) Prior Exposure-Other 0.110 0.116
36
(1.99)** (1.88)* Cognitive Ability-CRT 0.019 -0.009 (0.44) (0.18) Impulsivity-iCRT 0.038 0.025 (0.83) (0.52) Impulsivity-BIS Non-Planning -0.008 -0.003 (1.15) (0.41) Financial Literacy -0.034 -0.042 (1.09) (1.22) Perceived Win Likelihood (PWL) 0.081 (6.50)*** Reported Role of Perceived Win Likelihood (RRPWL) -0.077 (6.49)*** Correct Number-Recruits Needed 0.063 (1.26) Correct Number-Concurrent Recruiters 0.010 (0.19) Legal -0.064 (1.35) Constant 0.138 0.265 (0.41) (0.71) R2 0.33 0.11 N 348 348 Note: Robust standard errors appear in parentheses. Asterisks denote the following: * p<0.1; ** p<0.05; *** p<0.01 † Results regarding the Intent to Treat estimate are qualitatively unchanged when using bootstrap sampling within the linear probability model or when estimating as a probit or logistic model. When using sample weights by population for Minnesota ZIP Codes, the ITT estimate remains statistically insignificant in both specifications. These estimation results are provided in Appendix A, tables A2-A5.
37
Table 5. Estimation Results for Linear Probability Model Analysis of Fraud Uptake – Intent to Treat with Treatment Heterogeneity†
Variables Dependent variable: Uptake (binary)
OLS with post-treatment
variables
OLS without post-treatment
variables Treatment 0.308 1.164 (0.49) (1.60) Age -0.003 -0.001 (1.26) (0.26) Male -0.052 -0.136 (0.64) (1.45) Some College 0.220 0.179 (1.77)* (0.98) Bachelor's Degree 0.298 0.260 (2.44)** (1.41) Graduate Degree 0.218 0.163 (1.63) (0.84) Hispanic 0.194 0.148 (1.62) (0.94) Caucasian 0.127 0.036 (1.47) (0.35) HH Income Category -0.046 -0.040 (2.14)** (1.49) Democrat -0.071 -0.164 (0.93) (1.75)* Percent Urban 0.131 0.089 (0.94) (0.53) Willingness to Take Risk-Investment 0.009 0.018 (0.71) (1.33) Willingness to Take Risk-Gambling 0.011 0.020 (0.86) (1.32) Perceived Risk-Investment -0.008 -0.002 (0.56) (0.16) Perceived Risk-Gambling 0.020 0.017 (1.80)* (1.56) Perceived Benefit-Investment 0.012 0.019 (0.89) (1.26) Perceived Benefit-Gambling -0.004 -0.008 (0.49) (0.74) Religiosity 0.052 0.042 (1.56) (1.00) Negative Life Event 0.142 0.134 (1.99)** (1.57) Prior Exposure-Self -0.059 -0.142 (0.71) (1.57) Prior Exposure-Other 0.051 0.059
38
(0.64) (0.61) Cognitive Ability-CRT 0.104 0.070 (1.62) (1.03) Impulsivity-iCRT 0.046 0.033 (0.75) (0.52) Impulsivity-BIS Non-Planning -0.012 0.002 (1.17) (0.16) Financial Literacy -0.072 -0.065 (1.77)* (1.33) Perceived Win Likelihood (PWL) 0.080 (6.39)*** Reported Role of Perceived Win Likelihood (RRPWL) -0.078 (6.84)*** Correct Number-Recruits Needed 0.035 (0.67) Correct Number-Concurrent Recruiters 0.006 (0.12) Legal -0.081 (1.64) Treatment x Age 0.003 0.002 (0.91) (0.45) Treatment x Male 0.060 0.126 (0.53) (1.01) Treatment x Some College -0.466 -0.458 (2.46)** (1.91)* Treatment x Bachelor’s Degree -0.492 -0.503 (2.80)*** (2.15)** Treatment x Graduate Degree -0.426 -0.473 (2.25)** (1.92)* Treatment x Hispanic -0.350 -0.216 (1.59) (0.89) Treatment x Caucasian -0.180 -0.059 (1.28) (0.40) Treatment x HH Income 0.056 0.045 (1.70)* (1.21) Treatment x Democrat 0.097 0.192 (0.91) (1.53) Treatment x Percent Urban -0.285 -0.394 (1.47) (1.77)* Treatment x Willingness to take Risk-Investment -0.014 -0.018 (0.77) (0.90) Treatment x Willingness to take Risk-Gambling -0.001 -0.017 (0.03) (0.79) Treatment x Perceived Risk-Investment 0.020 0.010 (1.01) (0.46) Treatment x Perceived Risk-Gambling -0.027 -0.027
39
(1.52) (1.44) Treatment x Perceived Benefit-Investment 0.011 -0.000 (0.66) (0.01) Treatment x Perceived Benefit-Gambling 0.008 0.014 (0.57) (0.94) Treatment x Religiosity 0.021 -0.004 (0.41) (0.06) Treatment x Negative Life Event -0.119 -0.132 (1.17) (1.13) Treatment x Prior Exposure-Self 0.065 0.187 (0.51) (1.35) Treatment x Prior Exposure-Other 0.105 0.079 (0.91) (0.59) Treatment x CRT -0.113 -0.106 (1.23) (1.05) Treatment x iCRT 0.023 0.028 (0.25) (0.30) Treatment x BIS Non-Planning 0.007 -0.010 (0.54) (0.64) Treatment x Financial Literacy 0.059 0.021 (0.98) (0.28) Constant -0.110 -0.458 (0.27) (0.96) R2 0.39 0.18 N 348 348
Note: Robust standard errors appear in parentheses. Asterisks denote the following: * p<0.1; ** p<0.05; *** p<0.01 † Results regarding treatment-education interactions are qualitatively unchanged when using bootstrap sampling within the linear probability model or when estimating as a probit or logistic model. In the second specification, the Democrat interaction is positive and statistically significant at the 10% level in the probit and logit estimations. In addition, the interaction between treatment and Perceived Risk of Gambling is negative and statistically significant at the 10% level in both probit specifications and in the first logit specification. When using sample weights by population for Minnesota ZIP Codes, the treatment-education interaction terms are just outside of statistical significance in the second specification but are statistically significant in the first specification. All results from alternative estimations are provided in Appendix A, Tables A6-A9.
40
Table 6. Estimation Results for Linear Probability Model Analysis of Fraud Uptake – Correlates of Uptake† Variables Dependent variable: Uptake (binary)
OLS (1)
OLS (2)
OLS (3)
Treatment -0.066 -0.054 (1.37) (1.22) Age -0.001 (0.66) Male -0.024 (0.47) Some College -0.055 (0.57) Bachelor's Degree 0.017 (0.18) Graduate Degree -0.054 (0.53) Hispanic -0.023 (0.19) Caucasian -0.001 (0.02) HH Income Category -0.022 (1.30) Democrat -0.039 (0.73) Percent Urban 0.029 (0.30) Willingness to Take Risk-Investment 0.003 (0.29) Willingness to Take Risk-Gambling 0.010 (1.13) Perceived Risk-Investment 0.004 (0.40) Perceived Risk-Gambling 0.008 (0.91) Perceived Benefit-Investment 0.017 0.017 0.021 (1.94)* (2.90)*** (3.79)*** Perceived Benefit-Gambling -0.002 (0.22) Religiosity 0.050 0.055 0.046 (2.04)** (2.54)** (2.26)** Negative Life Event 0.072 (1.47) Prior Exposure-Self -0.059 (0.99) Prior Exposure-Other 0.110 0.091 0.079 (1.99)** (2.06)** (1.94)*
41
Cognitive Ability-CRT 0.019 (0.44) Impulsivity-iCRT 0.038 (0.83) Impulsivity-BIS Non-Planning -0.008 (1.15) Financial Literacy -0.034 (1.09) Perceived Win Likelihood (PWL) 0.081 0.084 0.079 (6.50)*** (7.58)*** (7.76)*** Reported Role of Perceived Win Likelihood (RRPWL) -0.077 -0.070 -0.069 (6.49)*** (6.42)*** (7.03)*** Correct Number-Recruits Needed 0.063 (1.26) Correct Number-Concurrent Recruiters 0.010 (0.19) Legal -0.064 (1.35) Constant 0.138 0.035 -0.008 (0.41) (0.29) (0.07) R2 0.33 0.30 0.27 N 348 365 447 Note: Robust standard errors appear in parentheses. Asterisks denote the following: * p<0.1; ** p<0.05; *** p<0.01 † Results regarding correlates are qualitatively unchanged when using bootstrap sampling within the linear probability model or when estimating as a probit or logistic model. When using sample weights by population for Minnesota ZIP Codes, Democrat (coef = -0.039) is statistically significant at the five percent level in all three specifications. Perceived benefits of investing, religiosity and prior exposure-others are just outside the range of statistical significance in the first specification and all but prior exposure become significant in the third specification. All maintain expected signs. All results from alternative estimations are provided in Appendix A, Tables A10-A13.
42
Table 7. Estimation Results for Linear Probability Model Analysis of Reported Role of Perceived Win Likelihood (RRPWL)† Variables Dependent Variable: RRPWL (ordinal, seven-point scale)
OLS (1)
OLS (2)
OLS (3)
Treatment -0.132 -0.036 (0.58) (0.17) Age -0.001 (0.08) Male 0.191 (0.77) Some College -0.163 (0.36) Bachelor's Degree -0.135 (0.31) Graduate Degree 0.022 (0.05) Hispanic 0.261 (0.43) Caucasian -0.144 (0.42) HH Income Category -0.051 (0.65) Democrat 0.384 (1.53) Percent Urban 0.802 0.823 0.709 (1.91)* (2.07)** (1.98)** Willingness to Take Risk-Investment 0.009 (0.22) Willingness to Take Risk-Gambling 0.003 (0.07) Perceived Risk-Investment 0.019 (0.44) Perceived Risk-Gambling 0.022 (0.76) Perceived Benefit-Investment -0.003 (0.08) Perceived Benefit-Gambling 0.050 (1.57) Religiosity 0.195 (1.58) Negative Life Event 0.159 (0.68) Prior Exposure-Self 0.076 (0.28) Prior Exposure-Other -0.177 (0.70)
43
Cognitive Ability-CRT 0.340 0.235 0.259 (1.99)** (2.35)** (2.92)*** Impulsivity-iCRT 0.138 (0.80) Impulsivity-BIS Non-Planning -0.055 -0.063 -0.052 (1.77)* (2.54)** (2.38)** Financial Literacy -0.017 (0.12) Constant 2.129 4.021 3.851 (1.49) (6.00)*** (6.58)*** R2 0.09 0.05 0.05 N 348 368 449 Note: Robust standard errors appear in parentheses. Asterisks denote the following: * p<0.1; ** p<0.05; *** p<0.01 † Results regarding Percent Urban as well as CRT and BIS scores are qualitatively unchanged when using bootstrap sampling within the linear probability model or when estimating as an ordered probit or ordered logit model. The same is true when using sample weights by population for Minnesota ZIP Codes. These alternative methods did identify religiosity as another statistically significant positive correlate of RRPWL. The estimation with sample weights also indicated that RRPWL is higher for those who perceive higher benefits from gambling, all else equal. All results from alternative estimations are provided in Appendix A, Tables A14-A17.
44
Table 8. Estimation Results for Linear Probability Model Analysis of Perceived Win Likelihood (PWL) †
Variables Dependent Variable: PWL (ordinal, seven-point scale)
OLS (1)
OLS (2)
OLS (3)
Treatment 0.213 0.203 (0.95) (0.96) Age 0.014 0.006 0.008 (1.65)* (0.92) (1.26) Male -0.346 -0.295 -0.192 (1.45) (1.32) (0.94) Some College -0.418 (0.88) Bachelor's Degree -0.377 (0.84) Graduate Degree -0.623 (1.33) Hispanic 0.600 (0.87) Caucasian -0.435 (1.29) HH Income Category -0.068 (0.88) Democrat -0.055 (0.21) Percent Urban -0.263 (0.59) Willingness to Take Risk-Investment 0.046 (1.04) Willingness to Take Risk-Gambling -0.003 (0.06) Perceived Risk-Investment -0.020 (0.44) Perceived Risk-Gambling 0.002 (0.06) Perceived Benefit-Investment 0.039 0.057 0.037 (0.90) (1.87)* (1.29) Perceived Benefit-Gambling 0.053 0.050 0.049 (1.66)* (1.80)* (1.90)* Religiosity 0.014 (0.12) Negative Life Event 0.165 (0.72) Prior Exposure-Self -0.120 (0.43) Prior Exposure-Other -0.096 (0.38)
45
Cognitive Ability-CRT -0.006 (0.03) Impulsivity-iCRT -0.008 (0.04) Impulsivity-BIS Non-Planning -0.005 (0.18) Financial Literacy -0.131 (0.87) Reported Role of Perceived Win Likelihood (RRPWL) -0.156 -0.142 -0.137 (2.84)*** (2.72)*** (2.84)*** Correct Number-Recruits Needed -0.413 -0.581 -0.379 (1.72)* (2.65)*** (1.92)* Correct Number-Concurrent Recruiters -0.314 -0.351 -0.323 (1.23) (1.54) (1.58) Legal 0.437 0.476 0.399 (1.89)* (2.12)** (1.99)** Constant 4.148 2.786 2.966 (2.45)** (4.95)*** (5.60)*** R2 0.16 0.11 0.08 N 348 367 449
Note: Robust standard errors appear in parentheses. Asterisks denote the following: * p<0.1; ** p<0.05; *** p<0.01 † Results regarding Perceived Benefits of Gambling and Investments, RRPWL, Correct Number of Recruits, and Legal are qualitatively unchanged when using bootstrap sampling within the linear probability model or when estimating as an ordered probit or ordered logit model. The same is true when using sample weights by population for Minnesota ZIP Codes. Alternative methods (ordered probit, ordered logit, and LPM with sampling weights) did identify age as another statistically significant positive correlate of PWL, with PWL rising with age. Both the ordered probit and ordered logit identified gender as a statistically significant correlate in the full model, with men estimating lower probabilities of winning on average, all else equal. The estimation with sample weights also indicated that PWL is lower for those who higher education, all else equal. All results from alternative estimations are provided in Appendix A, Tables A18-A21.
46
Table 9. Uptake Percentage by Education and Treatment Status
UPTAKE High School Some Bachelor’s Graduate Percentage (n) Or Less College Degree Degree Control 37.5% 45.5% 59.2% 36.5% (16) (44) (71) (52) Treatment 62.5% 42.1% 46.5% 32.3% (16) (38) (71) (62)
47
Table A1. Estimation Results for Linear Probability Model Analysis of Fraud Uptake – Alternate Measures of Religion
Variables Dependent variable: Uptake (binary)
OLS with both
religion variables
OLS with only
Religiosity
OLS with only
Service Attendance
Age -0.002 -0.002 -0.002 (0.96) (0.99) (1.03) Male -0.073 -0.073 -0.078 (1.53) (1.54) (1.67)* Some College -0.082 -0.082 -0.090 (1.01) (1.01) (1.08) Bachelor's Degree -0.033 -0.032 -0.023 (0.43) (0.43) (0.29) Graduate Degree -0.093 -0.093 -0.082 (1.08) (1.07) (0.93) Hispanic -0.026 -0.026 -0.014 (0.24) (0.24) (0.13) Caucasian -0.000 -0.001 0.016 (0.01) (0.01) (0.24) HH Income Category -0.018 -0.018 -0.018 (1.18) (1.18) (1.24) Democrat -0.044 -0.044 -0.053 (0.92) (0.91) (1.11) Percent Urban 0.111 0.110 0.097 (1.17) (1.18) (1.07) Willingness to Take Risk-Investment 0.005 0.005 0.005 (0.64) (0.64) (0.61) Willingness to Take Risk-Gambling 0.007 0.007 0.007 (0.78) (0.80) (0.81) Perceived Risk-Investment 0.009 0.009 0.009 (1.04) (1.07) (1.10) Perceived Risk-Gambling 0.008 0.008 0.009 (1.12) (1.13) (1.26) Perceived Benefit-Investment 0.018 0.018 0.019 (2.26)** (2.31)** (2.41)** Perceived Benefit-Gambling 0.001 0.001 0.000 (0.10) (0.10) (0.03) Religiosity 0.048 0.045 (1.31) (1.98)** Religious Service Attendance -0.002 0.013 (0.12) (1.42) Negative Life Event 0.043 0.044 0.043 (0.99) (1.00) (0.98) Prior Exposure-Self -0.056 -0.056 -0.047
48
(1.02) (1.03) (0.86) Prior Exposure-Other 0.098 0.098 0.083 (1.96)* (1.96)* (1.67)* Cognitive Ability-CRT 0.019 0.020 0.016 (0.47) (0.48) (0.39) Impulsivity-iCRT 0.034 0.034 0.038 (0.82) (0.83) (0.92) Impulsivity-BIS Non-Planning -0.003 -0.003 -0.000 (0.48) (0.46) (0.07) Financial Literacy -0.008 -0.009 -0.006 (0.30) (0.30) (0.22) Perceived Win Likelihood (PWL) 0.080 0.080 0.079 (7.14)*** (7.14)*** (7.06)*** Reported Role of Perceived Win Likelihood (RRPWL) -0.079 -0.079 -0.078 (7.47)*** (7.47)*** (7.47)*** Correct Number-Recruits Needed 0.034 0.034 0.029 (0.76) (0.76) (0.64) Correct Number-Concurrent Recruiters 0.053 0.054 0.056 (1.13) (1.14) (1.20) Legal -0.050 -0.050 -0.048 (1.14) (1.14) (1.10) Constant -0.171 -0.174 -0.187 (0.58) (0.59) (0.64) R2 0.31 0.31 0.30 N 424 424 428
Note: Robust standard errors appear in parentheses. Asterisks denote the following: * p<0.1; ** p<0.05; *** p<0.01
49
Table A2. Estimation Results for Linear Probability Model Analysis of Fraud Uptake – Intent to Treat with Bootstrap Sampling
Variables Dependent variable: Uptake (binary)
OLS with post-treatment variables
OLS without post-treatment variables
Treatment -0.066 -0.035 (1.40) (0.71) Age -0.001 -0.000 (0.72) (0.00) Male -0.024 -0.071 (0.43) (1.13) Some College -0.055 -0.080 (0.57) (0.69) Bachelor's Degree 0.017 -0.006 (0.17) (0.05) Graduate Degree -0.054 -0.110 (0.56) (1.00) Hispanic -0.023 0.000 (0.15) (0.00) Caucasian -0.001 -0.020 (0.02) (0.27) HH Income Category -0.022 -0.023 (1.34) (1.29) Democrat -0.039 -0.075 (0.78) (1.32) Percent Urban 0.029 -0.065 (0.29) (0.52) Willingness to Take Risk-Investment 0.003 0.005 (0.31) (0.64) Willingness to Take Risk-Gambling 0.010 0.010 (1.00) (0.86) Perceived Risk-Investment 0.004 0.001 (0.36) (0.06) Perceived Risk-Gambling 0.008 0.006 (0.87) (0.67) Perceived Benefit-Investment 0.017 0.020 (1.68)* (1.70)* Perceived Benefit-Gambling -0.002 -0.002 (0.22) (0.28) Religiosity 0.050 0.034 (2.21)** (1.24) Negative Life Event 0.072 0.070 (1.44) (1.21) Prior Exposure-Self -0.059 -0.072 (1.00) (1.14)
50
Prior Exposure-Other 0.110 0.116 (1.67)* (1.58) Cognitive Ability-CRT 0.019 -0.009 (0.38) (0.16) Impulsivity-iCRT 0.038 0.025 (0.74) (0.48) Impulsivity-BIS Non-Planning -0.008 -0.003 (1.14) (0.39) Financial Literacy -0.034 -0.042 (1.20) (1.31) Perceived Win Likelihood (PWL) 0.081 (6.64)*** Reported Role of Perceived Win Likelihood (RRPWL) -0.077 (6.89)*** Correct Number-Recruits Needed 0.063 (1.24) Correct Number-Concurrent Recruiters 0.010 (0.18) Legal -0.064 (1.30) Constant 0.138 0.265 (0.37) (0.62) R2 0.33 0.11 N 348 348
Note: Robust standard errors appear in parentheses. Asterisks denote the following: * p<0.1; ** p<0.05; *** p<0.01
51
Table A3. Estimation Results for Logistic Analysis of Fraud Uptake – Intent to Treat
Variables Dependent variable: Uptake (binary)
Logistic with post-treatment
variables
Logistic without post-treatment
variables Treatment -0.363 -0.168 (1.28) (0.70) Age -0.006 0.000 (0.55) (0.04) Male -0.140 -0.330 (0.46) (1.28) Some College -0.405 -0.337 (0.78) (0.69) Bachelor's Degree -0.023 -0.027 (0.05) (0.06) Graduate Degree -0.483 -0.500 (0.91) (0.97) Hispanic -0.077 0.003 (0.12) (0.00) Caucasian 0.062 -0.077 (0.15) (0.22) HH Income Category -0.157 -0.105 (1.48) (1.30) Democrat -0.187 -0.318 (0.61) (1.21) Percent Urban 0.308 -0.261 (0.56) (0.55) Willingness to Take Risk-Investment 0.017 0.026 (0.35) (0.61) Willingness to Take Risk-Gambling 0.059 0.049 (0.91) (1.03) Perceived Risk-Investment 0.020 0.002 (0.38) (0.05) Perceived Risk-Gambling 0.034 0.030 (0.79) (0.78) Perceived Benefit-Investment 0.107 0.089 (2.13)** (2.07)** Perceived Benefit-Gambling -0.002 -0.009 (0.05) (0.26) Religiosity 0.359 0.161 (2.38)** (1.27) Negative Life Event 0.381 0.315 (1.32) (1.31) Prior Exposure-Self -0.424 -0.339 (1.18) (1.15) Prior Exposure-Other 0.789 0.530
52
(2.37)** (1.95)* Cognitive Ability-CRT 0.074 -0.042 (0.30) (0.20) Impulsivity-iCRT 0.209 0.105 (0.81) (0.52) Impulsivity-BIS Non-Planning -0.058 -0.015 (1.48) (0.47) Financial Literacy -0.187 -0.186 (1.11) (1.26) Perceived Win Likelihood (PWL) 0.469 (5.83)*** Reported Role of Perceived Win Likelihood (RRPWL) -0.472 (5.97)*** Correct Number-Recruits Needed 0.391 (1.30) Correct Number-Concurrent Recruiters 0.083 (0.28) Legal -0.456 (1.55) Constant -1.909 -1.173 (1.06) (0.74) N 348 348
Note: Robust standard errors appear in parentheses. Asterisks denote the following: * p<0.1; ** p<0.05; *** p<0.01
53
Table A4. Estimation Results of Probit Analysis of Fraud Uptake – Intent to Treat
Variables Dependent variable: Uptake (binary)
Probit with post-
treatment variables
Probit without post-
treatment variables
Treatment -0.199 -0.102 (1.24) (0.70) Age -0.003 0.000 (0.55) (0.06) Male -0.105 -0.201 (0.60) (1.29) Some College -0.238 -0.214 (0.78) (0.71) Bachelor's Degree 0.008 -0.017 (0.03) (0.06) Graduate Degree -0.291 -0.310 (0.92) (1.00) Hispanic -0.011 0.027 (0.03) (0.08) Caucasian 0.014 -0.037 (0.06) (0.17) HH Income Category -0.089 -0.066 (1.50) (1.34) Democrat -0.117 -0.204 (0.66) (1.29) Percent Urban 0.154 -0.159 (0.48) (0.55) Willingness to Take Risk-Investment 0.005 0.015 (0.18) (0.60) Willingness to Take Risk-Gambling 0.038 0.030 (1.07) (1.04) Perceived Risk-Investment 0.008 -0.000 (0.26) (0.01) Perceived Risk-Gambling 0.021 0.018 (0.88) (0.78) Perceived Benefit-Investment 0.066 0.055 (2.31)** (2.13)** Perceived Benefit-Gambling -0.002 -0.005 (0.09) (0.27) Religiosity 0.200 0.097 (2.31)** (1.27) Negative Life Event 0.211 0.199 (1.28) (1.36) Prior Exposure-Self -0.244 -0.209 (1.19) (1.16) Prior Exposure-Other 0.425 0.328
54
(2.23)** (1.98)** Cognitive Ability-CRT 0.044 -0.024 (0.32) (0.19) Impulsivity-iCRT 0.123 0.067 (0.86) (0.54) Impulsivity-BIS Non-Planning -0.032 -0.009 (1.44) (0.47) Financial Literacy -0.113 -0.116 (1.14) (1.26) Perceived Win Likelihood (PWL) 0.270 (6.20)*** Reported Role of Perceived Win Likelihood (RRPWL) -0.274 (6.36)*** Correct Number-Recruits Needed 0.218 (1.26) Correct Number-Concurrent Recruiters 0.037 (0.21) Legal -0.236 (1.43) Constant -1.056 -0.694 (0.99) (0.71) N 348 348
Note: Robust standard errors appear in parentheses. Asterisks denote the following: * p<0.1; ** p<0.05; *** p<0.01
55
Table A5. Estimation Results of Linear Probability Model Analysis of Fraud Uptake – Intent to Treat using Sample Weights (based on Minnesota ZIP Code Population)
Variables Dependent variable: Uptake (binary)
OLS with post-
treatment variables
OLS without post-
treatment variables
Treatment -0.005 0.025 (0.09) (0.39) Age -0.002 -0.001 (0.91) (0.41) Male -0.032 -0.078 (0.49) (1.13) Some College -0.053 -0.141 (0.47) (1.13) Bachelor's Degree 0.010 -0.064 (0.10) (0.54) Graduate Degree 0.009 -0.073 (0.08) (0.58) Hispanic 0.006 -0.023 (0.04) (0.15) Caucasian -0.098 -0.107 (1.18) (1.23) HH Income Category -0.028 -0.034 (1.32) (1.60) Democrat -0.132 -0.185 (2.09)** (2.69)*** Percent Urban 0.054 -0.116 (0.26) (0.51) Willingness to Take Risk-Investment -0.005 -0.003 (0.49) (0.27) Willingness to Take Risk-Gambling 0.001 -0.007 (0.09) (0.59) Perceived Risk-Investment 0.005 0.001 (0.43) (0.06) Perceived Risk-Gambling 0.006 0.001 (0.55) (0.06) Perceived Benefit-Investment 0.018 0.020 (1.64) (1.66)* Perceived Benefit-Gambling 0.001 0.001 (0.08) (0.11) Religiosity 0.045 0.029 (1.50) (0.85) Negative Life Event 0.006 0.023 (0.09) (0.35) Prior Exposure-Self -0.029 -0.039
56
(0.43) (0.51) Prior Exposure-Other 0.097 0.104 (1.50) (1.51) Cognitive Ability-CRT -0.006 -0.035 (0.12) (0.66) Impulsivity-iCRT 0.044 0.041 (0.88) (0.81) Impulsivity-BIS Non-Planning -0.004 0.000 (0.46) (0.01) Financial Literacy -0.021 -0.009 (0.56) (0.23) Perceived Win Likelihood (PWL) 0.072 (4.59)*** Reported Role of Perceived Win Likelihood (RRPWL) -0.072 (5.05)*** Correct Number-Recruits Needed 0.042 (0.66) Correct Number-Concurrent Recruiters 0.023 (0.35) Legal -0.034 (0.59) Constant 0.344 0.702 (0.82) (1.48) R2 0.33 0.14 N 318 318
Note: Robust standard errors appear in parentheses. Asterisks denote the following: * p<0.1; ** p<0.05; *** p<0.01
57
Table A6. Estimation Results of Linear Probability Model Analysis of Fraud Uptake – Intent to Treat with Treatment Heterogeneity and Bootstrap Sampling
Variables Dependent variable: Uptake (binary)
OLS with post-
treatment variables
OLS with post-
treatment variables
Treatment 0.308 1.164 (0.37) (1.27) Age -0.003 -0.001 (1.32) (0.26) Male -0.052 -0.136 (0.58) (1.37) Some College 0.220 0.179 (1.85)* (0.98) Bachelor's Degree 0.298 0.260 (2.25)** (1.30) Graduate Degree 0.218 0.163 (1.62) (0.85) Hispanic 0.194 0.148 (1.11) (0.77) Caucasian 0.127 0.036 (1.44) (0.31) HH Income Category -0.046 -0.040 (1.89)* (1.41) Democrat -0.071 -0.164 (0.82) (1.70)* Percent Urban 0.131 0.089 (0.84) (0.50) Willingness to Take Risk-Investment 0.009 0.018 (0.71) (1.41) Willingness to Take Risk-Gambling 0.011 0.020 (0.73) (1.17) Perceived Risk-Investment -0.008 -0.002 (0.52) (0.16) Perceived Risk-Gambling 0.020 0.017 (1.57) (1.40) Perceived Benefit-Investment 0.012 0.019 (0.78) (1.13) Perceived Benefit-Gambling -0.004 -0.008 (0.41) (0.70) Religiosity 0.052 0.042 (1.48) (0.86) Negative Life Event 0.142 0.134 (1.98)** (1.64) Prior Exposure-Self -0.059 -0.142 (0.69) (1.61)
58
Prior Exposure-Other 0.051 0.059 (0.56) (0.56) Cognitive Ability-CRT 0.104 0.070 (1.37) (0.94) Impulsivity-iCRT 0.046 0.033 (0.65) (0.48) Impulsivity-BIS Non-Planning -0.012 0.002 (1.04) (0.16) Financial Literacy -0.072 -0.065 (1.92)* (1.32) Perceived Win Likelihood (PWL) 0.080 (6.23)*** Reported Role of Perceived Win Likelihood (RRPWL) -0.078 (6.50)*** Correct Number-Recruits Needed 0.035 (0.65) Correct Number-Concurrent Recruiters 0.006 (0.12) Legal -0.081 (1.57) Treatment x Age 0.003 0.002 (0.95) (0.45) Treatment x Male 0.060 0.126 (0.47) (0.91) Treatment x Some College -0.466 -0.458 (2.19)** (1.68)* Treatment x Bachelor’s Degree -0.492 -0.503 (2.45)** (1.88)* Treatment x Graduate Degree -0.426 -0.473 (1.89)* (1.72)* Treatment x Hispanic -0.350 -0.216 (1.31) (0.74) Treatment x Caucasian -0.180 -0.059 (1.17) (0.36) Treatment x HH Income 0.056 0.045 (1.51) (1.18) Treatment x Democrat 0.097 0.192 (0.79) (1.40) Treatment x Percent Urban -0.285 -0.394 (1.35) (1.74)* Treatment x Willingness to take Risk-Investment -0.014 -0.018 (0.73) (0.89) Treatment x Willingness to take Risk-Gambling -0.001 -0.017 (0.02) (0.72) Treatment x Perceived Risk-Investment 0.020 0.010 (0.88) (0.41)
59
Treatment x Perceived Risk-Gambling -0.027 -0.027 (1.41) (1.34) Treatment x Perceived Benefit-Investment 0.011 -0.000 (0.61) (0.01) Treatment x Perceived Benefit-Gambling 0.008 0.014 (0.58) (0.98) Treatment x Religiosity 0.021 -0.004 (0.45) (0.06) Treatment x Negative Life Event -0.119 -0.132 (1.17) (1.21) Treatment x Prior Exposure-Self 0.065 0.187 (0.53) (1.44) Treatment x Prior Exposure-Other 0.105 0.079 (0.95) (0.63) Treatment x CRT -0.113 -0.106 (1.19) (1.15) Treatment x iCRT 0.023 0.028 (0.23) (0.28) Treatment x BIS Non-Planning 0.007 -0.010 (0.46) (0.60) Treatment x Financial Literacy 0.059 0.021 (0.95) (0.27) Constant -0.110 -0.458 (0.20) (0.77) R2 0.39 0.18 N 348 348
Note: Robust standard errors appear in parentheses. Asterisks denote the following: * p<0.1; ** p<0.05; *** p<0.01
60
Table A7. Estimation Results of Logistic Analysis of Fraud Uptake – Intent to Treat with Treatment Heterogeneity
Variables Dependent variable: Uptake (binary)
Logit with post-
treatment variables
Logit with post-
treatment variables
Treatment 1.640 5.914 (0.40) (1.72)* Age -0.023 -0.002 (1.43) (0.14) Male -0.575 -0.718 (1.05) (1.70)* Some College 1.525 0.916 (1.91)* (1.11) Bachelor's Degree 1.924 1.269 (2.82)*** (1.53) Graduate Degree 1.378 0.789 (1.65)* (0.92) Hispanic 1.151 0.830 (1.44) (1.03) Caucasian 0.947 0.200 (1.63) (0.39) HH Income Category -0.352 -0.197 (2.27)** (1.59) Democrat -0.303 -0.801 (0.60) (1.88)* Percent Urban 0.806 0.444 (0.89) (0.58) Willingness to Take Risk-Investment 0.074 0.089 (1.08) (1.37) Willingness to Take Risk-Gambling 0.055 0.122 (0.52) (1.52) Perceived Risk-Investment -0.065 -0.008 (0.80) (0.12) Perceived Risk-Gambling 0.121 0.093 (1.90)* (1.73)* Perceived Benefit-Investment 0.080 0.097 (0.95) (1.38) Perceived Benefit-Gambling -0.020 -0.036 (0.35) (0.76) Religiosity 0.435 0.228 (1.88)* (1.15) Negative Life Event 1.060 0.689 (2.32)** (1.81)* Prior Exposure-Self -0.648 -0.756 (1.10) (1.74)*
61
Prior Exposure-Other 0.614 0.355 (1.25) (0.79) Cognitive Ability-CRT 0.648 0.343 (1.55) (1.11) Impulsivity-iCRT 0.248 0.147 (0.57) (0.49) Impulsivity-BIS Non-Planning -0.100 -0.001 (1.55) (0.03) Financial Literacy -0.488 -0.328 (1.91)* (1.48) Perceived Win Likelihood (PWL) 0.515 (5.66)*** Reported Role of Perceived Win Likelihood (RRPWL) -0.547 (5.80)*** Correct Number-Recruits Needed 0.268 (0.77) Correct Number-Concurrent Recruiters -0.009 (0.03) Legal -0.630 (2.02)** Treatment x Age 0.028 0.008 (1.26) (0.41) Treatment x Male 0.908 0.675 (1.18) (1.19) Treatment x Some College -3.318 -2.238 (2.68)*** (2.01)** Treatment x Bachelor’s Degree -3.217 -2.414 (3.02)*** (2.24)** Treatment x Graduate Degree -2.854 -2.265 (2.44)** (2.01)** Treatment x Hispanic -2.081 -1.114 (1.50) (0.91) Treatment x Caucasian -1.026 -0.279 (1.20) (0.39) Treatment x HH Income 0.366 0.213 (1.71)* (1.25) Treatment x Democrat 0.492 0.986 (0.75) (1.72)* Treatment x Percent Urban -1.998 -1.960 (1.50) (1.84)* Treatment x Willingness to take Risk-Investment -0.125 -0.091 (1.19) (0.99) Treatment x Willingness to take Risk-Gambling 0.021 -0.105 (0.12) (1.00) Treatment x Perceived Risk-Investment 0.130 0.041 (1.12) (0.42)
62
Treatment x Perceived Risk-Gambling -0.174 -0.135 (1.67)* (1.58) Treatment x Perceived Benefit-Investment 0.081 -0.001 (0.72) (0.01) Treatment x Perceived Benefit-Gambling 0.055 0.067 (0.67) (0.99) Treatment x Religiosity 0.119 -0.028 (0.35) (0.10) Treatment x Negative Life Event -1.067 -0.701 (1.56) (1.33) Treatment x Prior Exposure-Self 0.674 0.947 (0.85) (1.50) Treatment x Prior Exposure-Other 0.537 0.327 (0.79) (0.54) Treatment x CRT -0.794 -0.532 (1.41) (1.18) Treatment x iCRT 0.177 0.122 (0.30) (0.29) Treatment x BIS Non-Planning 0.059 -0.036 (0.66) (0.52) Treatment x Financial Literacy 0.436 0.131 (1.21) (0.40) Constant -3.148 -4.983 (1.15) (2.05)** N 348 348
Note: Robust standard errors appear in parentheses. Asterisks denote the following: * p<0.1; ** p<0.05; *** p<0.01
63
Table A8. Estimation Results of Probit Analysis of Fraud Uptake – Intent to Treat with Treatment Heterogeneity
Variables Dependent variable: Uptake (binary)
Probit with post-
treatment variables
Probit with post-
treatment variables
Treatment 1.110 3.666 (0.50) (1.78)* Age -0.013 -0.002 (1.44) (0.18) Male -0.335 -0.451 (1.13) (1.80)* Some College 0.893 0.546 (1.97)** (1.12) Bachelor's Degree 1.153 0.762 (2.80)*** (1.56) Graduate Degree 0.757 0.478 (1.59) (0.93) Hispanic 0.707 0.528 (1.51) (1.07) Caucasian 0.519 0.131 (1.51) (0.42) HH Income Category -0.214 -0.121 (2.46)** (1.64) Democrat -0.122 -0.489 (0.44) (1.94)* Percent Urban 0.411 0.274 (0.82) (0.62) Willingness to Take Risk-Investment 0.038 0.053 (0.95) (1.38) Willingness to Take Risk-Gambling 0.032 0.075 (0.51) (1.55) Perceived Risk-Investment -0.041 -0.007 (0.91) (0.16) Perceived Risk-Gambling 0.074 0.058 (2.09)** (1.80)* Perceived Benefit-Investment 0.049 0.062 (1.07) (1.48) Perceived Benefit-Gambling -0.010 -0.023 (0.30) (0.80) Religiosity 0.254 0.136 (1.99)** (1.18) Negative Life Event 0.576 0.432 (2.31)** (1.91)* Prior Exposure-Self -0.397 -0.466 (1.23) (1.77)*
64
Prior Exposure-Other 0.308 0.206 (1.11) (0.78) Cognitive Ability-CRT 0.349 0.206 (1.58) (1.11) Impulsivity-iCRT 0.128 0.089 (0.56) (0.49) Impulsivity-BIS Non-Planning -0.057 -0.000 (1.63) (0.01) Financial Literacy -0.272 -0.195 (1.89)* (1.47) Perceived Win Likelihood (PWL) 0.291 (6.44)*** Reported Role of Perceived Win Likelihood (RRPWL) -0.312 (6.86)*** Correct Number-Recruits Needed 0.136 (0.70) Correct Number-Concurrent Recruiters 0.000 (0.00) Legal -0.340 (1.96)** Treatment x Age 0.016 0.006 (1.30) (0.48) Treatment x Male 0.460 0.436 (1.14) (1.29) Treatment x Some College -1.898 -1.371 (2.80)*** (2.08)** Treatment x Bachelor’s Degree -1.865 -1.465 (3.10)*** (2.31)** Treatment x Graduate Degree -1.581 -1.391 (2.40)** (2.09)** Treatment x Hispanic -1.242 -0.682 (1.56) (0.94) Treatment x Caucasian -0.614 -0.177 (1.23) (0.41) Treatment x HH Income 0.237 0.133 (2.02)** (1.29) Treatment x Democrat 0.202 0.597 (0.55) (1.76)* Treatment x Percent Urban -1.123 -1.222 (1.54) (1.95)* Treatment x Willingness to take Risk-Investment -0.078 -0.057 (1.32) (1.06) Treatment x Willingness to take Risk-Gambling 0.004 -0.064 (0.05) (1.02) Treatment x Perceived Risk-Investment 0.074 0.026 (1.16) (0.45)
65
Treatment x Perceived Risk-Gambling -0.108 -0.086 (2.01)** (1.77)* Treatment x Perceived Benefit-Investment 0.053 -0.001 (0.86) (0.02) Treatment x Perceived Benefit-Gambling 0.028 0.041 (0.61) (1.01) Treatment x Religiosity 0.036 -0.019 (0.20) (0.12) Treatment x Negative Life Event -0.552 -0.426 (1.56) (1.37) Treatment x Prior Exposure-Self 0.441 0.581 (0.99) (1.54) Treatment x Prior Exposure-Other 0.316 0.218 (0.82) (0.61) Treatment x CRT -0.433 -0.321 (1.41) (1.20) Treatment x iCRT 0.105 0.081 (0.34) (0.31) Treatment x BIS Non-Planning 0.037 -0.022 (0.78) (0.54) Treatment x Financial Literacy 0.220 0.073 (1.08) (0.37) Constant -1.745 -3.038 (1.11) (2.07)** N 348 348
Note: Robust standard errors appear in parentheses. Asterisks denote the following: * p<0.1; ** p<0.05; *** p<0.01
66
Table A9. Estimation Results of Linear Probability Model Analysis of Fraud Uptake – Intent to Treat and Treatment Heterogeneity using Sample Weights (based on Minnesota ZIP Code Population)
Variables Dependent variable: Uptake (binary)
OLS with post-
treatment variables
OLS with post-
treatment variables
Treatment -0.631 0.640 (0.85) (0.72) Age -0.004 -0.000 (1.46) (0.10) Male -0.109 -0.210 (1.06) (1.87)* Some College 0.239 0.068 (1.62) (0.31) Bachelor's Degree 0.315 0.132 (2.29)** (0.61) Graduate Degree 0.265 0.120 (1.75)* (0.53) Hispanic 0.106 0.000 (0.71) (0.00) Caucasian -0.025 -0.137 (0.23) (1.22) HH Income Category -0.047 -0.041 (1.91)* (1.42) Democrat -0.111 -0.275 (1.26) (2.68)*** Percent Urban -0.019 -0.040 (0.08) (0.13) Willingness to Take Risk-Investment -0.005 0.008 (0.36) (0.48) Willingness to Take Risk-Gambling -0.002 0.002 (0.12) (0.11) Perceived Risk-Investment -0.007 0.003 (0.51) (0.16) Perceived Risk-Gambling 0.020 0.015 (1.39) (1.03) Perceived Benefit-Investment 0.011 0.019 (0.70) (1.07) Perceived Benefit-Gambling 0.005 0.003 (0.45) (0.26) Religiosity 0.056 0.021 (1.33) (0.39) Negative Life Event 0.044 0.030 (0.51) (0.30) Prior Exposure-Self -0.098 -0.184
67
(1.00) (1.68)* Prior Exposure-Other 0.114 0.151 (1.24) (1.36) Cognitive Ability-CRT 0.027 -0.025 (0.41) (0.37) Impulsivity-iCRT -0.014 -0.010 (0.22) (0.14) Impulsivity-BIS Non-Planning -0.013 -0.000 (1.17) (0.02) Financial Literacy -0.060 -0.003 (1.23) (0.04) Perceived Win Likelihood (PWL) 0.076 (4.78)*** Reported Role of Perceived Win Likelihood (RRPWL) -0.079 (5.82)*** Correct Number-Recruits Needed 0.041 (0.63) Correct Number-Concurrent Recruiters 0.018 (0.27) Legal -0.080 (1.36) Treatment x Age 0.004 0.001 (1.02) (0.22) Treatment x Male 0.118 0.173 (0.86) (1.16) Treatment x Some College -0.456 -0.387 (2.08)** (1.40) Treatment x Bachelor’s Degree -0.494 -0.415 (2.49)** (1.57) Treatment x Graduate Degree -0.373 -0.363 (1.80)* (1.31) Treatment x Hispanic -0.119 -0.015 (0.43) (0.05) Treatment x Caucasian -0.105 0.072 (0.66) (0.43) Treatment x HH Income 0.048 0.024 (1.17) (0.54) Treatment x Democrat 0.042 0.203 (0.34) (1.40) Treatment x Percent Urban 0.316 -0.073 (0.70) (0.15) Treatment x Willingness to take Risk-Investment -0.003 -0.013 (0.17) (0.56) Treatment x Willingness to take Risk-Gambling 0.010 -0.012 (0.46) (0.51) Treatment x Perceived Risk-Investment 0.027 0.010
68
(1.26) (0.40) Treatment x Perceived Risk-Gambling -0.034 -0.032 (1.55) (1.40) Treatment x Perceived Benefit-Investment 0.014 0.000 (0.65) (0.02) Treatment x Perceived Benefit-Gambling -0.004 0.001 (0.27) (0.08) Treatment x Religiosity 0.016 0.025 (0.25) (0.33) Treatment x Negative Life Event -0.108 -0.075 (0.87) (0.53) Treatment x Prior Exposure-Self 0.210 0.326 (1.41) (2.02)** Treatment x Prior Exposure-Other -0.050 -0.134 (0.38) (0.90) Treatment x CRT -0.037 0.007 (0.37) (0.07) Treatment x iCRT 0.121 0.116 (1.24) (1.12) Treatment x BIS Non-Planning 0.013 -0.003 (0.85) (0.16) Treatment x Financial Literacy 0.048 -0.037 (0.68) (0.42) Constant 0.546 0.183 (1.05) (0.31) R2 0.39 0.20 N 318 318
Note: Robust standard errors appear in parentheses. Asterisks denote the following: * p<0.1; ** p<0.05; *** p<0.01
69
Table A10. Estimation Results of Linear Probability Model Analysis of Fraud Uptake – Correlates of Uptake with Bootstrap Sampling
Variables Dependent variable: Uptake (binary)
OLS (1)
OLS (2)
OLS (3)
Treatment -0.066 -0.054 (1.40) (1.44) Age -0.001 (0.72) Male -0.024 (0.43) Some College -0.055 (0.57) Bachelor's Degree 0.017 (0.17) Graduate Degree -0.054 (0.56) Hispanic -0.023 (0.15) Caucasian -0.001 (0.02) HH Income Category -0.022 (1.34) Democrat -0.039 (0.78) Percent Urban 0.029 (0.29) Willingness to Take Risk-Investment 0.003 (0.31) Willingness to Take Risk-Gambling 0.010 (1.00) Perceived Risk-Investment 0.004 (0.36) Perceived Risk-Gambling 0.008 (0.87) Perceived Benefit-Investment 0.017 0.017 0.021 (1.68)* (3.27)*** (3.52)*** Perceived Benefit-Gambling -0.002 (0.22) Religiosity 0.050 0.055 0.046 (2.21)** (2.86)*** (2.12)** Negative Life Event 0.072 (1.44) Prior Exposure-Self -0.059 (1.00) Prior Exposure-Other 0.110 0.091 0.079 (1.67)* (2.11)** (1.75)*
70
Cognitive Ability-CRT 0.019 (0.38) Impulsivity-iCRT 0.038 (0.74) Impulsivity-BIS Non-Planning -0.008 (1.14) Financial Literacy -0.034 (1.20) Perceived Win Likelihood (PWL) 0.081 0.084 0.079 (6.64)*** (8.14)*** (7.23)*** Reported Role of Perceived Win Likelihood (RRPWL) -0.077 -0.070 -0.069 (6.89)*** (7.25)*** (7.10)*** Correct Number-Recruits Needed 0.063 (1.24) Correct Number-Concurrent Recruiters 0.010 (0.18) Legal -0.064 (1.30) Constant 0.138 0.035 -0.008 (0.37) (0.33) (0.07) R2 0.33 0.30 0.27 N 348 365 447
Note: Robust standard errors appear in parentheses. Asterisks denote the following: * p<0.1; ** p<0.05; *** p<0.01
71
Table A11. Estimation Results of Logistic Analysis of Fraud Uptake – Correlates of Uptake Variables Dependent variable: Uptake (binary)
Logit (1)
Logit (1)
Logit (3)
Treatment -0.363 -0.286 (1.28) (1.12) Age -0.006 (0.55) Male -0.140 (0.46) Some College -0.405 (0.78) Bachelor's Degree -0.023 (0.05) Graduate Degree -0.483 (0.91) Hispanic -0.077 (0.12) Caucasian 0.062 (0.15) HH Income Category -0.157 (1.48) Democrat -0.187 (0.61) Percent Urban 0.308 (0.56) Willingness to Take Risk-Investment 0.017 (0.35) Willingness to Take Risk-Gambling 0.059 (0.91) Perceived Risk-Investment 0.020 (0.38) Perceived Risk-Gambling 0.034 (0.79) Perceived Benefit-Investment 0.107 0.099 0.118 (2.13)** (2.84)*** (3.71)*** Perceived Benefit-Gambling -0.002 (0.05) Religiosity 0.359 0.345 0.278 (2.38)** (2.67)*** (2.37)** Negative Life Event 0.381 (1.32) Prior Exposure-Self -0.424 (1.18) Prior Exposure-Other 0.789 0.547 0.458 (2.37)** (2.11)** (2.00)** Cognitive Ability-CRT 0.074
72
(0.30) Impulsivity-iCRT 0.209 (0.81) Impulsivity-BIS Non-Planning -0.058 (1.48) Financial Literacy -0.187 (1.11) Perceived Win Likelihood (PWL) 0.469 0.454 0.419 (5.83)*** (6.45)*** (6.91)*** Reported Role of Perceived Win Likelihood (RRPWL) -0.472 -0.397 -0.385 (5.97)*** (6.12)*** (6.88)*** Correct Number-Recruits Needed 0.391 (1.30) Correct Number-Concurrent Recruiters 0.083 (0.28) Legal -0.456 (1.55) Constant -1.909 -2.725 -2.899 (1.06) (3.91)*** (4.49)*** N 348 365 447 Note: Robust standard errors appear in parentheses. Asterisks denote the following: * p<0.1; ** p<0.05; *** p<0.01
73
Table A12. Estimation Results of Probit Analysis of Fraud Uptake – Correlates of Uptake Variables Dependent variable: Uptake (binary)
Probit (1)
Probit (1)
Probit (3)
Treatment -0.199 -0.157 (1.24) (1.05) Age -0.003 (0.55) Male -0.105 (0.60) Some College -0.238 (0.78) Bachelor's Degree 0.008 (0.03) Graduate Degree -0.291 (0.92) Hispanic -0.011 (0.03) Caucasian 0.014 (0.06) HH Income Category -0.089 (1.50) Democrat -0.117 (0.66) Percent Urban 0.154 (0.48) Willingness to Take Risk-Investment 0.005 (0.18) Willingness to Take Risk-Gambling 0.038 (1.07) Perceived Risk-Investment 0.008 (0.26) Perceived Risk-Gambling 0.021 (0.88) Perceived Benefit-Investment 0.066 0.061 0.072 (2.31)** (3.01)*** (3.88)*** Perceived Benefit-Gambling -0.002 (0.09) Religiosity 0.200 0.202 0.166 (2.31)** (2.65)*** (2.41)** Negative Life Event 0.211 (1.28) Prior Exposure-Self -0.244 (1.19) Prior Exposure-Other 0.425 0.310 0.268 (2.23)** (2.04)** (1.99)** Cognitive Ability-CRT 0.044
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(0.32) Impulsivity-iCRT 0.123 (0.86) Impulsivity-BIS Non-Planning -0.032 (1.44) Financial Literacy -0.113 (1.14) Perceived Win Likelihood (PWL) 0.270 0.265 0.249 (6.20)*** (6.72)*** (7.22)*** Reported Role of Perceived Win Likelihood (RRPWL) -0.274 -0.236 -0.234 (6.36)*** (6.38)*** (7.18)*** Correct Number-Recruits Needed 0.218 (1.26) Correct Number-Concurrent Recruiters 0.037 (0.21) Legal -0.236 (1.43) Constant -1.056 -1.645 -1.749 (0.99) (4.07)*** (4.66)*** N 348 365 447
Note: Robust standard errors appear in parentheses. Asterisks denote the following: * p<0.1; ** p<0.05; *** p<0.01
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Table A13. Estimation Results of Linear Probability Model Analysis of Fraud Uptake – Correlates of Uptake using Sample Weights (based on Minnesota ZIP Code Population)
Variables Dependent variable: Uptake (binary)
OLS (1)
OLS (2)
OLS (3)
Treatment -0.005 -0.013 (0.09) (0.24) Age -0.002 (0.91) Male -0.032 (0.49) Some College -0.053 (0.47) Bachelor's Degree 0.010 (0.10) Graduate Degree 0.009 (0.08) Hispanic 0.006 (0.04) Caucasian -0.098 (1.18) HH Income Category -0.028 (1.32) Democrat -0.132 (2.09)** Percent Urban 0.054 (0.26) Willingness to Take Risk-Investment -0.005 (0.49) Willingness to Take Risk-Gambling 0.001 (0.09) Perceived Risk-Investment 0.005 (0.43) Perceived Risk-Gambling 0.006 (0.55) Perceived Benefit-Investment 0.018 0.013 0.014 (1.64) (1.77)* (2.04)** Perceived Benefit-Gambling 0.001 (0.08) Religiosity 0.045 0.056 0.054 (1.50) (2.14)** (2.25)** Negative Life Event 0.006 (0.09) Prior Exposure-Self -0.029 (0.43) Prior Exposure-Other 0.097 0.087 0.072 (1.50) (1.60) (1.45)
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Cognitive Ability-CRT -0.006 (0.12) Impulsivity-iCRT 0.044 (0.88) Impulsivity-BIS Non-Planning -0.004 (0.46) Financial Literacy -0.021 (0.56) Perceived Win Likelihood (PWL) 0.072 0.078 0.078 (4.59)*** (5.46)*** (6.13)*** Reported Role of Perceived Win Likelihood (RRPWL) -0.072 -0.070 -0.066 (5.05)*** (5.22)*** (5.46)*** Correct Number-Recruits Needed 0.042 (0.66) Correct Number-Concurrent Recruiters 0.023 (0.35) Legal -0.034 (0.59) Constant 0.344 0.098 0.055 (0.82) (0.68) (0.41) R2 0.33 0.28 0.26 N 318 332 405
Note: Robust standard errors appear in parentheses. Asterisks denote the following: * p<0.1; ** p<0.05; *** p<0.01
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Table A14. Estimation Results for Linear Probability Model Analysis of Reported Role of Perceived Win Likelihood (RRPWL) with Bootstrap Sampling
Variables Dependent Variable: RRPWL (ordinal, 7-point scale)
OLS (1)
OLS (2)
OLS (3)
Treatment -0.132 -0.036 (0.61) (0.15) Age -0.001 (0.09) Male 0.191 (0.79) Some College -0.163 (0.35) Bachelor's Degree -0.135 (0.29) Graduate Degree 0.022 (0.04) Hispanic 0.261 (0.42) Caucasian -0.144 (0.34) HH Income Category -0.051 (0.68) Democrat 0.384 (1.80)* Percent Urban 0.802 0.823 0.709 (1.97)** (2.27)** (1.87)* Willingness to Take Risk-Investment 0.009 (0.22) Willingness to Take Risk-Gambling 0.003 (0.07) Perceived Risk-Investment 0.019 (0.42) Perceived Risk-Gambling 0.022 (0.85) Perceived Benefit-Investment -0.003 (0.08) Perceived Benefit-Gambling 0.050 (1.63) Religiosity 0.195 (1.73)* Negative Life Event 0.159 (0.70) Prior Exposure-Self 0.076 (0.28) Prior Exposure-Other -0.177 (0.69)
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Cognitive Ability-CRT 0.340 0.235 0.259 (1.88)* (2.25)** (2.96)*** Impulsivity-iCRT 0.138 (0.81) Impulsivity-BIS Non-Planning -0.055 -0.063 -0.052 (1.89)* (2.79)*** (2.30)** Financial Literacy -0.017 (0.12) Constant 2.129 4.021 3.851 (1.67)* (6.65)*** (6.41)*** R2 0.09 0.05 0.05 N 348 368 449
Note: Robust standard errors appear in parentheses. Asterisks denote the following: * p<0.1; ** p<0.05; *** p<0.01
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Table A15. Estimation Results for Ordered Logistic Analysis of Reported Role of Perceived Win Likelihood (RRPWL)
Variables Dependent Variable: RRPWL (ordinal, 7-point scale)
Logit (1)
Logit (2)
Logit (3)
Treatment -0.083 -0.013 (0.40) (0.07) Age -0.002 (0.26) Male 0.190 (0.82) Some College -0.158 (0.40) Bachelor's Degree -0.166 (0.44) Graduate Degree -0.016 (0.04) Hispanic 0.350 (0.62) Caucasian -0.101 (0.33) HH Income Category -0.072 (0.98) Democrat 0.343 (1.46) Percent Urban 0.768 0.757 0.614 (1.97)** (2.00)** (1.86)* Willingness to Take Risk-Investment 0.002 (0.06) Willingness to Take Risk-Gambling 0.008 (0.17) Perceived Risk-Investment 0.003 (0.07) Perceived Risk-Gambling 0.016 (0.62) Perceived Benefit-Investment -0.002 (0.05) Perceived Benefit-Gambling 0.043 (1.46) Religiosity 0.215 (1.83)* Negative Life Event 0.146 (0.69) Prior Exposure-Self 0.089 (0.36) Prior Exposure-Other -0.091 (0.40)
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Cognitive Ability-CRT 0.287 0.187 0.217 (1.96)** (2.18)** (2.85)*** Impulsivity-iCRT 0.091 (0.61) Impulsivity-BIS Non-Planning -0.060 -0.057 -0.047 (2.00)** (2.57)** (2.46)** Financial Literacy -0.034 (0.29) cut 1 Constant -0.907 -1.982 -1.897 (0.70) (3.22)*** (3.62)*** cut 2 Constant 0.229 -0.863 -0.731 (0.18) (1.42) (1.42) cut 3 Constant 0.922 -0.165 -0.040 (0.72) (0.27) (0.08) cut 4 Constant 1.396 0.270 0.392 (1.09) (0.44) (0.76) cut 5 Constant 1.898 0.741 0.852 (1.49) (1.23) (1.67)* cut 6 Constant 2.788 1.616 1.782 (2.19)** (2.66)*** (3.45)*** N 348 368 449
Note: Robust standard errors appear in parentheses. Asterisks denote the following: * p<0.1; ** p<0.05; *** p<0.01
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Table A16. Estimation Results for Ordered Probit Analysis of Reported Role of Perceived Win Likelihood (RRPWL)
Variables Dependent Variable: RRPWL (ordinal, 7-point scale)
Probit (1)
Probit (2)
Probit (3)
Treatment -0.034 0.009 (0.29) (0.08) Age -0.001 (0.17) Male 0.099 (0.76) Some College -0.132 (0.55) Bachelor's Degree -0.160 (0.70) Graduate Degree -0.043 (0.18) Hispanic 0.224 (0.69) Caucasian -0.049 (0.28) HH Income Category -0.036 (0.87) Democrat 0.196 (1.50) Percent Urban 0.454 0.444 0.375 (2.08)** (2.07)** (1.97)** Willingness to Take Risk-Investment 0.002 (0.09) Willingness to Take Risk-Gambling 0.003 (0.10) Perceived Risk-Investment 0.008 (0.32) Perceived Risk-Gambling 0.011 (0.70) Perceived Benefit-Investment 0.001 (0.03) Perceived Benefit-Gambling 0.026 (1.56) Religiosity 0.125 (1.92)* Negative Life Event 0.068 (0.57) Prior Exposure-Self 0.049 (0.36) Prior Exposure-Other -0.050 (0.39)
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Cognitive Ability-CRT 0.181 0.116 0.133 (2.09)** (2.25)** (2.89)*** Impulsivity-iCRT 0.066 (0.74) Impulsivity-BIS Non-Planning -0.032 -0.033 -0.027 (1.94)* (2.50)** (2.30)** Financial Literacy -0.032 (0.46) cut 1 Constant -0.345 -1.157 -1.090 (0.47) (3.19)*** (3.48)*** cut 2 Constant 0.313 -0.506 -0.410 (0.43) (1.41) (1.32) cut 3 Constant 0.738 -0.075 0.017 (1.02) (0.21) (0.06) cut 4 Constant 1.029 0.195 0.286 (1.43) (0.54) (0.92) cut 5 Constant 1.332 0.482 0.565 (1.85)* (1.36) (1.85)* cut 6 Constant 1.842 0.986 1.097 (2.55)** (2.75)*** (3.55)*** N 348 368 449
Note: Robust standard errors appear in parentheses. Asterisks denote the following: * p<0.1; ** p<0.05; *** p<0.01
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Table A17. Estimation Results for Linear Probability Model Analysis of Reported Role of Perceived Win Likelihood (RRPWL) using Sample Weights (based on Minnesota ZIP Code Population)
Variables Dependent Variable: RRPWL (ordinal, 7-point scale)
OLS (1)
OLS (2)
OLS (3)
Treatment -0.265 -0.165 (0.98) (0.65) Age 0.005 (0.42) Male 0.401 (1.41) Some College 0.171 (0.32) Bachelor's Degree 0.032 (0.06) Graduate Degree 0.018 (0.03) Hispanic 0.527 (0.79) Caucasian -0.230 (0.59) HH Income Category -0.016 (0.18) Democrat 0.416 (1.42) Percent Urban 1.980 1.587 1.498 (2.08)** (1.97)** (2.00)** Willingness to Take Risk-Investment -0.002 (0.03) Willingness to Take Risk-Gambling 0.038 (0.73) Perceived Risk-Investment 0.016 (0.30) Perceived Risk-Gambling 0.034 (0.93) Perceived Benefit-Investment -0.002 (0.05) Perceived Benefit-Gambling 0.066 (1.68)* Religiosity 0.283 (2.00)** Negative Life Event -0.241 (0.85) Prior Exposure-Self -0.045 (0.14) Prior Exposure-Other -0.094
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(0.33) Cognitive Ability-CRT 0.413 0.169 0.174 (2.01)** (1.43) (1.66)* Impulsivity-iCRT 0.226 (1.15) Impulsivity-BIS Non-Planning -0.063 -0.055 -0.044 (1.74)* (1.89)* (1.72)* Financial Literacy -0.108 (0.64) Constant 0.329 3.303 3.063 (0.18) (3.16)*** (3.31)*** R2 0.11 0.04 0.03 N 318 337 410
Note: Robust standard errors appear in parentheses. Asterisks denote the following: * p<0.1; ** p<0.05; *** p<0.01
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Table A18. Estimation Results for Linear Probability Model Analysis of Perceived Win Likelihood (PWL) with Bootstrap Sampling
Variables Dependent Variable: PWL (ordinal, 7-point scale)
OLS (1)
OLS (2)
OLS (3)
Treatment 0.204 0.203 (0.97) (0.94) Age 0.017 0.006 0.008 (1.86)* (0.92) (1.34) Male -0.240 -0.295 -0.192 (1.09) (1.17) (0.93) Some College -0.376 (0.74) Bachelor's Degree -0.378 (0.78) Graduate Degree -0.630 (1.35) Hispanic 0.532 (0.71) Caucasian -0.534 (1.48) HH Income Category -0.082 (1.14) Democrat -0.123 (0.49) Percent Urban -0.274 (0.54) Willingness to Take Risk-Investment 0.048 (1.22) Willingness to Take Risk-Gambling -0.005 (0.12) Perceived Risk-Investment -0.025 (0.57) Perceived Risk-Gambling -0.010 (0.26) Perceived Benefit-Investment 0.037 0.057 0.037 (0.86) (2.00)** (1.26) Perceived Benefit-Gambling 0.068 0.050 0.049 (2.09)** (1.68)* (1.84)* Religiosity -0.007 (0.05) Negative Life Event 0.118 (0.41) Prior Exposure-Self -0.136 (0.51) Prior Exposure-Other -0.093 (0.35)
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Cognitive Ability-CRT -0.076 (0.42) Impulsivity-iCRT -0.020 (0.10) Impulsivity-BIS Non-Planning -0.012 (0.35) Financial Literacy -0.197 (1.58) Reported Role of Perceived Win Likelihood (RRPWL) -0.187 -0.142 -0.137 (3.84)*** (3.00)*** (2.89)*** Correct Number-Recruits Needed -0.581 -0.379 (2.56)** (2.01)** Correct Number-Concurrent Recruiters -0.351 -0.323 (1.47) (1.67)* Legal 0.476 0.399 (2.26)** (2.36)** Constant 4.820 2.786 2.966 (2.69)*** (4.46)*** (5.71)*** R2 0.13 0.11 0.08 N 348 367 449
Note: Robust standard errors appear in parentheses. Asterisks denote the following: * p<0.1; ** p<0.05; *** p<0.01
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Table A19. Estimation Results for Ordered Logit Analysis of Perceived Win Likelihood (PWL)
Variables Dependent Variable: PWL (ordinal, 7-point scale)
Logit (1)
Logit (2)
Logit (3)
Treatment 0.281 0.317 (1.38) (1.63) Age 0.014 0.005 0.006 (1.72)* (0.83) (1.07) Male -0.436 -0.354 -0.239 (1.92)* (1.74)* (1.30) Some College -0.514 (1.19) Bachelor's Degree -0.520 (1.27) Graduate Degree -0.631 (1.54) Hispanic 0.449 (0.68) Caucasian -0.394 (1.35) HH Income Category -0.095 (1.33) Democrat -0.012 (0.05) Percent Urban -0.158 (0.39) Willingness to Take Risk-Investment 0.039 (0.95) Willingness to Take Risk-Gambling -0.008 (0.17) Perceived Risk-Investment -0.026 (0.57) Perceived Risk-Gambling 0.003 (0.09) Perceived Benefit-Investment 0.035 0.045 0.029 (0.85) (1.60) (1.13) Perceived Benefit-Gambling 0.051 0.041 0.043 (1.63) (1.53) (1.71)* Religiosity 0.087 (0.73) Negative Life Event 0.073 (0.35) Prior Exposure-Self -0.186 (0.75) Prior Exposure-Other -0.018 (0.07)
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Cognitive Ability-CRT -0.030 (0.17) Impulsivity-iCRT -0.018 (0.09) Impulsivity-BIS Non-Planning -0.002 (0.08) Financial Literacy -0.116 (0.88) Reported Role of Perceived Win Likelihood (RRPWL) -0.159 -0.144 -0.133 (3.11)*** (3.00)*** (3.02)*** Correct Number-Recruits Needed -0.438 -0.578 -0.383 (1.96)** (2.87)*** (2.18)** Correct Number-Concurrent Recruiters -0.260 -0.290 -0.253 (1.11) (1.41) (1.38) Legal 0.460 0.478 0.375 (2.09)** (2.32)** (2.08)** cut1 Constant -1.905 -0.683 -0.863 (1.18) (1.31) (1.80)* cut2 Constant -1.222 -0.050 -0.211 (0.76) (0.10) (0.44) cut3 Constant -0.513 0.686 0.504 (0.32) (1.34) (1.06) cut4 Constant 0.230 1.394 1.193 (0.14) (2.72)*** (2.51)** cut5 Constant 0.737 1.884 1.644 (0.46) (3.64)*** (3.44)*** cut6 Constant 1.191 2.328 2.164 (0.74) (4.47)*** (4.48)*** N 348 367 449
Note: Robust standard errors appear in parentheses. Asterisks denote the following: * p<0.1; ** p<0.05; *** p<0.01
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Table A20. Estimation Results for Ordered Probit Analysis of Perceived Win Likelihood (PWL)
Variables Dependent Variable: PWL (ordinal, 7-point scale)
Probit (1)
Probit (2)
Probit (3)
Treatment 0.163 0.159 (1.37) (1.39) Age 0.008 0.004 0.004 (1.74)* (0.97) (1.22) Male -0.217 -0.183 -0.126 (1.67)* (1.52) (1.16) Some College -0.232 (0.95) Bachelor's Degree -0.227 (1.00) Graduate Degree -0.338 (1.44) Hispanic 0.254 (0.72) Caucasian -0.242 (1.37) HH Income Category -0.047 (1.14) Democrat -0.014 (0.10) Percent Urban -0.134 (0.56) Willingness to Take Risk-Investment 0.024 (1.06) Willingness to Take Risk-Gambling -0.002 (0.07) Perceived Risk-Investment -0.018 (0.74) Perceived Risk-Gambling 0.001 (0.04) Perceived Benefit-Investment 0.017 0.028 0.016 (0.73) (1.70)* (1.09) Perceived Benefit-Gambling 0.030 0.026 0.026 (1.67)* (1.71)* (1.82)* Religiosity 0.035 (0.52) Negative Life Event 0.076 (0.62) Prior Exposure-Self -0.116 (0.79) Prior Exposure-Other 0.008 (0.06)
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Cognitive Ability-CRT -0.005 (0.05) Impulsivity-iCRT -0.000 (0.00) Impulsivity-BIS Non-Planning -0.000 (0.03) Financial Literacy -0.059 (0.77) Reported Role of Perceived Win Likelihood (RRPWL) -0.094 -0.083 -0.078 (3.14)*** (2.90)*** (2.98)*** Correct Number-Recruits Needed -0.220 -0.317 -0.204 (1.70)* (2.66)*** (1.95)* Correct Number-Concurrent Recruiters -0.146 -0.165 -0.146 (1.09) (1.36) (1.34) Legal 0.238 0.258 0.210 (1.90)* (2.14)** (1.97)** cut1 Constant -1.096 -0.355 -0.495 (1.23) (1.14) (1.75)* cut2 Constant -0.691 0.024 -0.104 (0.78) (0.08) (0.37) cut3 Constant -0.264 0.472 0.335 (0.30) (1.54) (1.19) cut4 Constant 0.182 0.898 0.754 (0.21) (2.94)*** (2.67)*** cut5 Constant 0.477 1.184 1.019 (0.54) (3.84)*** (3.60)*** cut6 Constant 0.731 1.431 1.309 (0.82) (4.62)*** (4.58)*** N 348 367 449
Note: Robust standard errors appear in parentheses. Asterisks denote the following: * p<0.1; ** p<0.05; *** p<0.01
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Table A21. Estimation Results for Linear Probability Model Analysis of Perceived Win Likelihood (PWL) using Sample Weights (based on Minnesota ZIPCode Population)
Variables Dependent Variable: PWL (ordinal, 7-point scale)
OLS (1)
OLS (2)
OLS (3)
Treatment 0.058 0.176 (0.22) (0.72) Age 0.023 0.013 0.016 (2.19)** (1.55) (2.04)** Male 0.034 -0.119 -0.025 (0.13) (0.46) (0.10) Some College -0.953 (1.78)* Bachelor's Degree -0.975 (1.94)* Graduate Degree -1.117 (2.13)** Hispanic 0.135 (0.18) Caucasian -0.538 (1.61) HH Income Category -0.121 (1.30) Democrat -0.267 (0.92) Percent Urban 0.235 (0.22) Willingness to Take Risk-Investment 0.025 (0.49) Willingness to Take Risk-Gambling -0.063 (1.33) Perceived Risk-Investment -0.047 (0.90) Perceived Risk-Gambling -0.038 (0.86) Perceived Benefit-Investment 0.011 0.035 0.020 (0.24) (1.01) (0.60) Perceived Benefit-Gambling 0.103 0.059 0.075 (2.69)*** (1.93)* (2.53)** Religiosity 0.117 (0.86) Negative Life Event -0.070 (0.28) Prior Exposure-Self -0.212 (0.67) Prior Exposure-Other 0.014 (0.05)
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Cognitive Ability-CRT 0.065 (0.29) Impulsivity-iCRT 0.241 (1.06) Impulsivity-BIS Non-Planning -0.038 (1.14) Financial Literacy -0.068 (0.42) Reported Role of Perceived Win Likelihood (RRPWL) -0.294 -0.225 -0.217 (4.62)*** (3.60)*** (3.78)*** Correct Number-Recruits Needed -0.796 -0.573 (2.99)*** (2.42)** Correct Number-Concurrent Recruiters -0.256 -0.215 (0.96) (0.88) Legal 0.677 0.435 (2.60)*** (1.86)* Constant 6.139 3.004 2.952 (2.95)*** (4.69)*** (4.81)*** R2 0.19 0.17 0.13 N 318 334 407
Note: Robust standard errors appear in parentheses. Asterisks denote the following: * p<0.1; ** p<0.05; *** p<0.01
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APPENDIX B
B.1 Survey Questionnaire
Note: Subjects answer these questions within a Google Form on an iPad.
Did you choose option A or B? (circle one) A or B
Please enter your age: _______
What is your gender? (circle one)
Male, Female, Other _________
What is your highest level of education? (circle one)
Some high school, High school diploma or GED, Associate's degree, Some college, no degree, Bachelor's degree, Graduate or professional degree, Other
What is your ethnicity? (circle one)
Hispanic or Latino, Not Hispanic or Latino
What is your racial background? (circle one)
American Indian or Alaska Native, Asian, Black or African American, Hawaiian or Other Pacific Islander, White, Multiracial, Other
Please enter your zip code: ________________
For each of the following statements, please indicate the likelihood that you would engage in the described activity or behavior if you were to find yourself in that situation.
Provide a rating from Extremely Unlikely to Extremely Likely, using the following scale:
1 2 3 4 5 6 7 Extremely Moderately Somewhat Not Sure Somewhat Moderately Extremely Unlikely Unlikely Unlikely Likely Likely Likely Betting a day’s income at the horse races 1 2 3 4 5 6 7 Investing 10% of your annual income in a moderate growth diversified fund 1 2 3 4 5 6 7 Betting a day's income at a casino or high-stakes poker game 1 2 3 4 5 6 7 Investing 5% of your annual income in a very speculative stock 1 2 3 4 5 6 7 Betting a day’s income on the outcome of a sporting event 1 2 3 4 5 6 7 Investing 10% of your annual income in a new business venture 1 2 3 4 5 6 7
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For each of the following statements, please indicate how risky you perceive each situation. Provide a rating from Not at all Risky to Extremely Risky, using the following scale: 1 2 3 4 5 6 7 Not at all Slightly Somewhat Moderately Risky Very Extremely Risky Risky Risky Risky Risky Risky Betting a day’s income at the horse races 1 2 3 4 5 6 7 Investing 10% of your annual income in a moderate growth diversified fund 1 2 3 4 5 6 7 Betting a day's income at a casino or high-stakes poker game 1 2 3 4 5 6 7 Investing 5% of your annual income in a very speculative stock 1 2 3 4 5 6 7 Betting a day’s income on the outcome of a sporting event 1 2 3 4 5 6 7 Investing 10% of your annual income in a new business venture 1 2 3 4 5 6 7 For each of the following statements, please indicate the benefits you would obtain from each situation. Provide a rating from 1 to 7, using the following scale: 1 2 3 4 5 6 7 No benefits Moderate Great At all Benefits Benefits Betting a day’s income at the horse races 1 2 3 4 5 6 7 Investing 10% of your annual income in a moderate growth diversified fund 1 2 3 4 5 6 7 Betting a day's income at a casino or high-stakes poker game 1 2 3 4 5 6 7 Investing 5% of your annual income in a very speculative stock 1 2 3 4 5 6 7 Betting a day’s income on the outcome of a sporting event 1 2 3 4 5 6 7 Investing 10% of your annual income in a new business venture 1 2 3 4 5 6 7 How religious do you consider yourself to be? (circle one) Not at all religious, Not too religious, Somewhat religious, Very religious, I don’t know How often do you attend religious services? (circle one)
Never, Less than once a year, Once a year, Several times a year, Once a month, Two to three times a month, Nearly every week, Every week, More than once a week
Which statement most closely reflects your political affiliation? (circle one)
Identify as Democrat, Lean toward Democrat, Identify as Republican, Lean toward Republican, Identify as Independent/Third Party, Lean toward Independent/Third Party, None of the above
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And for statistical purposes only, which of the following best describes your annual household income? Less than $20,000, Between $20,000 - $40,000, Between $40,000 - $60,000, Between $60,000 - $80,000, Between $80,000 - $100,000, Over $100,000, Don’t Know
Below are three items that vary in difficulty. Answer as many as you can. (1) A desk and a chair cost $110 in total. The desk costs $100 more than the chair. How much
does the chair cost? _________ dollars
(2) If it take 5 ovens 5 minutes to make 5 pizzas, how long would it take 100 ovens to make 100 pizzas? ___________ minutes
(3) In a lake, there is algae. Every day, the algae doubles in size. If it takes 48 days for the algae
to cover the entire lake, how long would it take for the algae to cover half of the lake? __________ days Have you seen these three questions before? (circle one) Yes, these exact questions, Yes, similar questions, No
In the past two years, have you experienced a serious negative life event, such as a divorce, the death of a family member or close friend, a serious injury or illness for you or a family member (physical or mental health), or the loss of a job?
Yes or No (circle one) On these next questions, if you do not immediately know the answer, please try to figure it out. If the chance of getting a disease is 10 percent, out of 1,000 people, how many would be expected to get the disease?
a. Less than 10 people b. 10 people c. More than 10 people d. Don’t know
A used car dealer is selling a car for $10,000. This is two-thirds of what the car cost new. How much did the car cost when it was new?
a. Less than $15,000 b. $15,000 c. More than $15,000 d. Don’t know
Let’s say you have $200 in a savings account. The account earns 10 percent interest per year. How much will you have in the account at the end of two years?
a. More than $240 b. Less than $240 c. $240 d. Don’t know
No matter what option you chose today (A or B), we would like to ask you some questions regarding an option you were asked to consider, the Airplane Game (Option B). You may refer back to the paper descriptions of options A and B.
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If you were to invest in the Airplane Game, what do you think your chances are of becoming a Captain and winning the $10?
a. above 50% chance of winning b. 40-49% c. 30-39% d. 20-29% e. 10-19% f. 5-9% g. below 5%
In order for you to become a Captain and win $10 in the Airplane Game, how many people would need to be recruited under you (by you or those under you)?
a. 3 people b. 9 people c. 27 people d. 39 people e. 40 or more people
If you were to invest in the Airplane Game, how many people (at a minimum) do you think would be recruiting to become a Captain at the same time as you? ___________ people When you were deciding whether to keep your $5 or enter the Airplane Game, how much did your chances of becoming a Captain (i.e., your odds of winning the Airplane Game) influence your decision? 1 2 3 4 5 6 7 Not at all Very little Somewhat Moderately Quite a lot Very Much Extremely Do you think the Airplane Game is legal? Yes or No (circle one) (After Debrief videos) Now that we have discussed pyramid schemes and warning signs, please think about your past experiences. Do you think that someone close to you (close family member or friend) has ever been recruited by or involved in a pyramid scheme? Yes or No (circle one) Do you think that you have ever been recruited by or involved in a pyramid scheme? Yes or No (circle one)
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B2. Experiment Protocol
• Potential subject expresses interest at experiment booth.
• Subject completes consent form and English language proficiency check.11
• When a space is available:
o The subject is given $5 in cash and a “Choice Task” handout (provided below in
Appendix B.3).
o The subject is seated at a station equipped with an iPad, headphones, and a pen,
with subject dividers in place.
o The subject is instructed that she can write on the page as desired and that she will
be entering her responses on the iPad and will only need the headphones near the
end of the experiment.
• The subject then completes the following:
o Enters a subject identification number, provided at the top of the choice task
handout.
o Reads the choice task handout and enters a decision, choosing Option A (keep the
$5) or Option B (invest the money in the Airplane Game).
o Answers the set of survey questions provided in Appendix B.1.
o Watches two short debrief videos, approximately two minutes each.
o Responds to two last questions regarding prior exposure to pyramid scheme fraud.
• At this point, the subject is instructed to raise her hand for assistance. A research assistant
then completes the following tasks with the subject:
o If the subject chose Option A, her hand is marked with a black marker, otherwise her
hand is marked with a blue marker.
11 A Spanish language version was also available but two potential subjects expressed interest and only one completed the full experiment so this data was not included in the experimental dataset.
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o The subject is then directed to the payment table. The research assistant at the
payment table notes the color marked on the subject’s hand.
If black, he instructs the subject to keep her $5.
If blue, he reminds the subject that she has chosen to invest in the Airplane
Game, collects the subject’s $5, and reminds the subject of the chances of
winning the Airplane Game described in the debrief video as 0.01 and 0.99
chances of winning and losing, respectively. He then asks the subject to draw
from the bag of marbles, where a green marble pays $10 (winning the
Airplane Game) and a red marble pays $1 (losing the Airplane Game). The
subject is paid, in cash, according to the marble drawn.
o The subject is then asked to record the payment received ($10, $5, or $1) on a
receipt log and the subject receives an educational brochure and a Principle
Investigator’s business card. If the subject has any questions or comments, she is
directed to the Principle Investigator.
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B3. Choice Task Handout
Note that the image below is the Choice Task handout for the treatment group. The control group received an identical handout except the bold first line regarding odds was absent.